Mr Putin has said he will be prime minister if Mr Medvedev is elected
Russians are voting on 2 March to elect a new president - the country's third since the collapse of the Soviet Union.
The incumbent, Vladimir Putin, is stepping down at the end of two four-year terms, as prescribed by the constitution.
First Deputy Prime Minister Dmitry Medvedev, 42, has Mr Putin's public backing as his preferred successor, and is regarded as almost certain to win.
What is at stake?
On paper, quite a lot. Under Russia's constitution, the presidency is by far the most powerful institution in the Russian state.
Apart from being head of state, the president is in overall charge of setting government policy. He can veto laws passed by parliament, which needs a two-thirds majority in both houses to overcome the president's opposition.
The president takes the lead in choosing the prime minister, and while parliament can reject his choice, it cannot insist on a candidate of its own. The president also appoints Russia's regional heads of government.
What are the rules?
To win, a candidate must get over 50% of the vote. Failing that, the two highest polling candidates go through to a second round, to be held 21 days after the first.
In order to run, candidates had either to be put forward by a party in parliament, or collect the signatures of two million voters.
Polling is staggered across Russia's 11 time zones. The first polling stations opened at 2000 GMT on 1 March in the far east, with the last closing in the far west at 1800 GMT on 2 March.
Around 109 million Russians are eligible to vote in Russia and abroad.
Who is standing?
Mr Medvedev has promised to continue Mr Putin's course
A close ally of Mr Putin, Mr Medvedev is the candidate of the pro-Kremlin United Russia party. It has a two-thirds majority in the lower house, the Duma. Opinion polls suggest he could win 60-80% of the vote.
Like Mr Putin and many of the president's allies, Mr Medvedev, who previously worked as a lawyer, hails from St Petersburg. However, he lacks Mr Putin's background in the security services, and is seen as more liberal.
While promising to continue Mr Putin's policies, he has called for less state intervention in the economy, as well as a greater focus on education and social welfare.
Credited with a great deal of economic experience, Mr Medvedev has promised to give Russia "decades of stable development", create a law-abiding society and fight corruption.
Mr Zyuganov, 63, has been the leader of the Communist Party of Russia since 1993, and is a long-standing fixture of post-Soviet opposition politics.
He came close to beating Boris Yeltsin in the 1996 election, and stood against Mr Putin in 2000. However, opinion polls currently give him only a 6-15% share of the vote.
Mr Zyuganov is a strong critic of Russia's post-Soviet economic reforms, and has described capitalism as "barbaric". He routinely rails against Russia's super-rich businessmen, the "oligarchs".
During his campaign, he has called for higher wages and pensions, more affordable housing, and the nationalisation of Russia's lucrative natural resources.
Another veteran of Russian politics, Mr Zhirinovsky, 61, is known for his brash and confrontational style.
He has been the leader of the Liberal Democratic Party of Russia since its foundation in 1990. Despite his party's name, Mr Zhirinovsky has strongly nationalist, anti-Western and authoritarian views. Polls suggest he could win around 10% of the vote.
He has a record of anti-Semitic outbursts, and has a tendency towards political stunts which appeal to popular sentiment. However, despite his maverick reputation, Mr Zhirinovsky avoids direct criticism of the Kremlin.
Building up Russia's military strength is his main political theme. On domestic policy, his manifesto promises Russians "just three projects - housing, good roads and food".
Mr Bogdanov, 38, is little known in Russia, and seen as something of a mystery candidate.
He leads the Democratic Party of Russia, which won 90,000 votes at the 2007 parliamentary elections - just over 1% of the total.
However, Mr Bogdanov is the only candidate to have qualified by collecting two million signatures. Some observers believe he is being sponsored by the Kremlin to split the opposition vote.
Mr Bogdanov describes his party as "liberal conservative". His main policy is to seek European Union membership for Russia.
What about Russia's liberal opposition?
None of Russia's liberal opposition parties has a candidate in the race. One opposition leader, former Prime Minister Mikhail Kasyanov, was barred from standing after the electoral authorities said signatures collected in his support had been forged.
Liberal opposition candidate Mikhail Kasyanov was barred from standing
Mr Kasyanov described the move as "purely political", while the Central Electoral Commission insisted it had acted in accordance with the law.
Another opposition leader, Boris Nemtsov, withdrew, saying the election's outcome had been predetermined. He had not got to the point of being registered as a candidate.
Will the election be free and fair?
The observer group of the Organisation for Security and Co-operation in Europe (OSCE) described Russia's last nationwide vote - the parliamentary election in December 2007 - as neither free nor fair.
In the run-up to these elections, opposition candidates complained that state-owned national television stations devoted an overwhelming amount of coverage to Dmitry Medvedev.
Are international observers there?
Yes - but only about 300 international observers for some 96,000 polling stations.
The process was overshadowed by the OSCE's decision to boycott the election; the organisation said that restrictions imposed by Russia on its monitors would have made it impossible to do their job.
Russia reacted angrily to the move, accusing the OSCE of making "ultimatums".
What will Mr Putin's role be after the election?
This has been the subject of intense speculation; Mr Putin at least partly dispelled some of the mystery by accepting an offer to become prime minister if Mr Medvedev is elected.
Some observers believe Mr Medvedev's candidacy is merely a way for Mr Putin to maintain influence after formally stepping down, and that the outgoing president will - as prime minister - continue to call the shots.
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