The 55-year-old was walking home from dinner with his girlfriend Anna Duritskaya when he was gunned down in Moscow on Friday.
Nemtsov had been arrested several times for speaking against Putin's government. The most recent arrests were in 2011 when he protested the results of parliamentary elections and in 2012 when tens of thousands protested against Putin.
In an interview with CNN's Anthony Bourdain last year, Nemtsov spoke of the deaths of other Kremlin critics, but said his fame offered some protection.
"I'm a well-known guy, and this is a safety because if something happens with me, it will be scandal not only in Moscow city but throughout the world," he said then.
After Nemtsov was shot, Putin condemned the killing and ordered three law enforcement agencies to investigate the shooting, the Kremlin said in a statement.
But critics of Putin have in the past suffered miserable fates.
Last year, a Moscow court sentenced five men to prison for the 2006 killing of Russian journalist and fierce Kremlin critic Anna Politkovskaya.
Business magnate Mikhail Khodorkovsky
accused Putin of corruption and spent 10 years in prison and labor camps.
Russian spy Alexander Litvinenko
accused state security services of organizing a coup to put Putin in power. He was poisoned by a lethal dose of radioactive polonium and died in London in 2006. No killer has been caught.
Wealth and corruption
In their 2014 interview, Nemtsov told Bourdain he believed Russia's existing power structure was like 19th century Russia, with one person in control and no real freedom of press, real competition or elections or an independent judiciary or rule of law.
"You are in the typical country of crony capitalism," he said. "If you have a good relationship with Putin and his people around, you will have a good relationship with governor or mayor -- it doesn't matter. If you are in the city you have a chance to raise money, to be successful ... you know, to buy real estate in the south of France or Switzerland, to open accounts in Swiss banks.
"But, if something happened between you and Putin and you are governor, you will be in jail."
Nemstov said in most places around the world, wealth provided opportunity and independence, but said that it was different in Russia.
"To be wealthy, you must be loyal. If you want to be independent, forget about business, forget about raising money," he said. "If you are rich, you are a slave. If you are rich, you are very much dependent."
Many people preferred to be able make money and not speak out, he said.
"This is a country of corruption," Nemtsov said. "For Putin's Russia, this is a system. This is not a problem."
"If you are corrupted, but you are loyal, and you serve the Kremlin, you are first of all rich and secondly you are in a very safe position."