Since I got both ships for my collection, Ushakov and Kutznezov, I have re newed my interest in contemporary navies. This mainly because it seems that the USN monopoly at least have potential challengers now; hegemony, as historical evidence always suggest, will come to a point of crisis.
This link is clarifying by itself, but will like to highlight several points:http://en.wikipedia.org/wiki/Russian_navy
The russians are expending a huge amount of money in refiting their naval forces. Forces that once challenged the NATO ones and were taking seriously by a threatened West that now sleeps thinking their biggest problem is climate change, gay rights and islamic inmigrants rights.
Recently approved, a rearmament program until 2015 puts, for the first time in Soviet and Russian history, the development of the navy on an equal footing with strategic nuclear forces. The program covering the period until 2015 is expected to replace 45% of the military inventory in the army and navy. Out of 4.9 trillion rubles ($192.16 billion) allocated for military rearmament, 25% will go into building new ships. "We are already building practically as many ships as we did in Soviet times," First Deputy Prime Minister Sergey Ivanov said during a visit to Severodvinsk in July 2007, "The problem now is not lack of money, but how to optimize production so that the navy can get new ships three, not five, years after laying them down."
Let's remember that russians can get, in theory, more from their money than the Americans: less project management fees, less expensive indirect charges, etc.
The recent improvement in the Russian economy has led to a significant rise in defence expenditure and an increase in numbers of ships under construction, focusing on submarines, such as the conventional Petersburg (Lada) class and nuclear Severodvinsk (Yasen) class. Some older ships have been refitted as well. Jane's Fighting Ships commented in 2004 that the construction programme was too focused on Cold War scenarios, given the submarine emphasis.  The Steregushchiy class corvettes, the lead ship of which was laid down on 21 December 2001, is the first new surface construction since the collapse of the Soviet Union, while the new Admiral Sergei Gorshkov class frigates marks the first attempt of the Navy to return to the construction of large blue water capable vessels.
In 2005 it was announced that the Russian Navy planned a class of 2-4 new aircraft carriers which could start construction in 2013-14 for initial service entry in 2017.  Jane's said it was not clear whether 'this was a funded programme'. New amphibious ships are planned as well. In mid-2007 the new Navy chief announced plans to reform the country's naval forces and build a blue-water navy with the world's second largest fleet of aircraft carriers, aiming to create 6 aircraft carrier strike groups in the next 20 years.
Three new SSBNs are now under construction, (the Dolgorukiy (Borey) class SSBNs), but the first has been under construction since 1996- its completion was expected in 2008. The lead Dolgorukiy Class unit Yuriy Dolgorukiy was launched in April 2007 and began sea trials in June 2009. The fourth unit is scheduled to be laid down in 2010 The mainstay of the SSBN force, the Delta IVs, joined the fleet in 1985-91. While the service life of an SSBN normally is twenty to twenty-five years, without maintenance, it may be as short as ten to fifteen years.
On September 24, 2008, Moscow a Russian lawmaker said that Russia could offer Ukraine contracts to build aircraft carriers for the Russian Navy. He commented on Russian Defense Minister Anatoliy Serdyukov's statement on Tuesday that Russia could make several lucrative proposals to Ukraine that could convince Kiev to allow Russia's Black Sea Fleet to remain in Sevastopol after 2017, when the lease on the naval base in the Crimea expires. "We can offer Ukraine extensive and lucrative opportunities in the sphere of shipbuilding. They have the Nikolaev shipyards that used to build aircraft carriers during Soviet times," said Vyacheslav Popov, a former commander of the Northern Fleet who now sits in the upper house of parliament. These shipyards are bankrupt and abandoned at present and with mutual consent we could help reactivate them," Popov said.
Russia currently does not have a facility capable of building aircraft carriers. The most promising sites for a future such facility are either St. Petersburg or Severodvinsk but significant capital improvements would be required.
Russian officials have been negotiating a purchase of four Mistral class amphibious assault ships. On 24 May 2010, the Russian Defense Minister said that Russia was in pre-contract discussions with Spain, Netherlands, and France on purchasing four Mistral-type ships. It was planned to have one ship built abroad, two with the participation of Russian shipbuilders, and at least one built in a Russian shipyard. The Defense Minister also said that the first ships of this type would be based in the Northern and Pacific Fleets. 
On April 28, 2010, The Ukrainian parliament ratified an agreement to lease the port of Sevastopol past the year 2017.
Look that the deal with western european countries is mentioned.
Expeditions and increase in activity
In the last years of the 1990s naval activity was very low. Even at the height of the Kosovo war crisis a planned task group deployment to the Mediterranean was reduced to the dispatch of the intelligence ship Liman. 2003 saw a major increase in activity, including several major exercises. A May joint exercise with the Indian Navy saw two Pacific Fleet destroyers and four vessels from the Black Sea Fleet, led by the Slava-class cruiser Moskva, deployed for three months into the Indian Ocean. The largest out-of-area deployment for a decade, the INDRA 2003 exercise, was highlighted by a series of missile launches by two Tu-160s and four Tu-95s, which made a 5,400 mile round trip flight from Engels-2 air base near Saratov to the exercise area. In August 2003 the Navy also participated in the Far Eastern exercise Vostok-2003, which saw the Slava-class cruiser Varyag and the Sovremennyy class destroyer Bystryy active, as well as an amphibious landing carried out by three Pacific Fleet Ropucha class LSTs. Warships and helicopters from the Japanese and South Korean navies also took part. The Northern Fleet followed in January 2004 when thirteen ships and seven submarines took part in exercises in the Barents Sea. The involvement of Admiral Kuznetsov and Kirov-class nuclear-powered cruiser Petr Velikiy was overshadowed however by two ballistic missile launch failures, made more embarrassing because President Vladimir Putin was afloat aboard the Typhoon-class SSBN Arkhangelsk to witness the tests. Neither of the Delta IV-class Novomoskovsk nor Kareliya were able to successfully launch what were apparently RSM-54 SLBMs. Former Navy Commander-in-Chief Vladimir Kuroyedov's early dismissal may have resulted from these gaffes. He was replaced by Admiral Vladimir Masorin in September 2005.
Embarrassment for the Navy had unfortunately continued, with a mine accident during rehearsals for the Baltic Fleet's celebration of Navy Day in St. Petersburg in July 2005 and the Priz class mini-submarine AS-28 having to be rescued by a joint British/U.S. effort using a Royal Navy unmanned submersible in the Far East in early August 2005. However exercises and operations continued - Peace Mission 2005 in August 2005 involved a new level of cooperation between Russia and the Chinese People's Liberation Army Navy. Two months later the Slava-class cruiser Varyag led Russian participation in INDRA 2005, held off Vishakapatnam between 14 and 20 October 2005. It included surface firings, air defence, and anti-submarine warfare (ASW) exercises.
Admiral Vladimir Vysotskiy became Commander-in-Chief of the Russian Navy on September 11, 2007, having moved up from the Northern Fleet, which he had commanded since September 2005.
On October 16, 2008, the speaker of Russia's upper house of parliament said that Russia could resume a naval presence in Yemen. Authorities in the Middle East country had been calling on Moscow to help fight piracy and possible terrorist threats. The U.S.S.R. had a major naval support base in the former socialist state of South Yemen, which merged with North Yemen in 1990 to form the present-day Yemen. Speaking to journalists in Sana, the capital of Yemen, Federation Council Speaker Sergey Mironov said the new direction of Russia's foreign and defense policies and an increase in its naval missions would be taken into consideration when making a decision on the request. "It's possible that the aspects of using Yemen ports not only for visits by Russian warships, but also for more strategic goals will be considered," he said.
Mironov also said a visit to Russia by the president of Yemen, Ali Abdullah Saleh, could take place in the near future and that the issue of military technical cooperation could be raised during his visit.
 North Atlantic and Mediterranean Sea
In February 2008 a Russian naval task force completed a two-month deployment in the Mediterranean Sea and the North Atlantic which started on December 4, 2007. The operation was the first large-scale Russian Navy deployment to the Atlantic and the Mediterranean in 15 years. The task force included the Kuznetsov-Class aircraft carrier Kuznetsov, the Udaloy-Class destroyers Admiral Levchenko and Admiral Chabanenko, and the Slava-Class guided missile cruiser Moskva, as well as auxiliary vessels. During the operation the navy practiced rescue and counter-terror operations, reconnaissance, and missile and bomb strikes on the (theoretical) enemy's naval task force. Over 40 Russian Air Force aircraft took part in joint exercises with the navy as well. Vice-Admiral Nikolay Maksimov, the Northern Fleet commander, said during the operations that the deployment was aimed at ensuring Russia's naval presence "in key operational areas of the world's oceans" and establishing conditions for secure Russian maritime navigation. "After this visit to the Mediterranean and France, the first in 15 years, we will establish a permanent presence in the region" he said. Admiral Vladimir Vysotskiy summed up the results in February saying: "What is important is that we have appeared [in the Atlantic and the Mediterranean] at a scheduled time and not just that we appeared there. We'll do all we can to build up our presence where Russia has strategic interests", adding that Russia intended to carry out similar missions once every six months.
In October, 2008, a naval task group from the Northern Fleet, comprising the nuclear-powered missile cruiser Pyotr Velikiy, the large ASW ship Admiral Chabanenko, and support ships, left their homeport of Severomorsk in northern Russia on September 22 and is currently in the northern Atlantic, having covered a distance of 1,000 nautical miles (2,000 km) in a week. "Having some spare time before a joint exercise with the Venezuelan navy, which is planned for November 2008, the warships will perform a number of tasks in the Mediterranean Sea and visit several Mediterranean ports, including Tripoli," the Navy's press service said in a statement. Russian warships are scheduled to participate in joint naval exercises with the Venezuelan navy in the Caribbean on November 10-14, in line with the 2008 training program, and in order to expand military cooperation with foreign navies. These exercises actually took place on 1 December.
October 11, 2008, Russian warships bound for Venezuela, including the nuclear-powered cruiser Pyotr Veliky (Peter the Great), put in Saturday at the Libyan port of Tripoli for refuelling.
From Venezuela the Petr Velikiy proceeded to a port call in Capetown, South Africa, then participated in the INDRA-2009 exercise off western India, briefly engaged in counter-piracy operations in the Gulf of Aden, and returned to its homeport of Severomorsk in March 2009.
In September 2008 It has been reported that Russia and Syria are conducting talks about permitting Russia to develop and enlarge the base in order to establish a stronger naval presence in the Mediterranean., and amidst the deteriorating Russia relations with the west in conjunction with the 2008 South Ossetia war and the plans to deploy US missile defense shield in Poland, it has even been asserted that president Assad has agreed to Tartus port’s conversion into a permanent Middle East base for Russia’s nuclear-armed warships. Moscow and Damascus additionally announced that it would be renovating the port, although there was no mention in the Syrian press.  On September 19, ten Russian warships have docked in Tartus,Syria. According to Lebanese-Syrian commentator Joseph Farah the flotilla which has been moved to Tartus consists of the Moskva cruiser and four nuclear missile submarines. According to Farah upgrades of the port facilities are already under way. Since 1992 the port has been in disrepair with only one of its three floating piers remaining operational,but the facilities now are being restored.
On September 22, 2008, Russian Navy spokesman Igor Dygalo said the nuclear-powered Peter the Great cruiser, accompanied by three other ships, sailed from the Northern Fleet's base of Severomorsk. The ships will cover about 15,000 nautical miles to conduct joint maneuvers with the Venezuelan navy. Dygalo refused to comment on Monday's report in the daily Izvestia claiming that the ships were to make a stopover in the Syrian port of Tartus on their way to Venezuela. Russian officials said the Soviet-era base there was being renovated to serve as a foothold for a permanent Russian navy presence in the Mediterranean. 
 Caribbean Sea
On September 8, 2008, it was announced that the Pyotr Velikiy would sail to the Caribbean Sea in order to participate in naval exercises with the Venezuelan Navy. This action would represent the first major Russian show of force in that sea since the end of the Cold War. On 22 September the Kirov class nuclear missile cruiser Petr Velikiy and the Udaloy class large anti-submarine ship Admiral Chabanenko, accompanied by support vessels, left their homeport of Severomorsk for naval exercises with Venezuela scheduled for early November 2008. 
On late November 25, 2008, A group of warships from Russia's Northern Fleet arrived at the Venezuelan port of La Guaira. "The Udaloy class destroyer Admiral Chabanenko has docked in port, while the Pyotr Veliky missile cruiser has dropped anchor off La Guaira," said Capt. 1st Rank Igor Dygalo
 East Africa: Somali Coast
On September 24, 2008, the Russian Neustrashimyy left its home base at Baltiysk, Kaliningrad Oblast, Russia, for counter-piracy operations near the Somali coast, said Russian Navy spokesman Captain 1st Rank Igor Dygalo. Moscow Interfax-Agenstvo Voyennykh Novostey 24 Sep 2008</ref>.
On November 19, 2008, Commander-in-Chief of the Russian Navy Admiral Vysotskiy, speaking to the official news agency, RIA Novosti, stated that the Russian Navy would send additional vessels to the area.
From January 11 through 17 March 2009, the Admiral Vinogradov took up the counter-piracy mission from the Neustrashimyy and upon completion took a course home to Vladivostok by way of a port visit to Djakarta, Indonesia 24-28 March 2009. 
From 26 April through 7 June 2009, the Pacific Fleet destroyer Admiral Panteleyev took up counter-piracy duties in the Gulf of Aden, having left Vladivostok at the end of March 2009 to relieve the Admiral Vinogradov. It returned to Vladivostok on 1 July. 
On 29 June 2009, the Pacific Fleet destroyer Admiral Tributs was preparing to depart Vladivostok to relieve Admiral Panteleyev for counter-piracy operations in the Gulf of Aden. Depending on the situation, the deployment could last from two to six months.
 Indian Ocean and Arabian Sea
On 11 January, 2009, Army General Makarov - Chief of the Russian General Staff - announced that the Kirov class nuclear-powered cruiser Petr Velikiy and five other ships would take part in exercises with the Indian Navy in late January 2009 
To underate or ignore the russian navy is a serious mistake. They are still thinking in a Cold War scenario and their build up is pointing that way.