The 115 cardinal-electors are shut off in the Sistine Chapel and a nearby residence until two-thirds agree on a leader for the world's 1.2bn Catholics.
Black smoke signalling an inconclusive first vote drew cheers from crowds in St Peter's Square on Tuesday evening.
There is no clear frontrunner to replace Pope Benedict XVI.
The 85-year-old stepped down last month, saying he was no longer strong enough to lead the Church, which is beset by problems ranging from a worldwide scandal over child sex abuse to allegations of corruption at the Vatican Bank.
Conclave timetable - all times GMT
08:30 - Prayer followed by voting in the Sistine Chapel. Black smoke will emerge if two morning ballots are inconclusive. White smoke will appear as soon as there is a positive outcome
Smoke could come any time between about 09:30 and 11:30
1130 - If no Pope is elected, cardinals go back to their residence for lunch
15:00 - Cardinals return to the Sistine Chapel for another two rounds of voting - smoke expected between 16:30 and 18:30
If there is no result by Friday, they will hold a day of prayer and reflection on Saturday before resuming the election
The cardinals will vote four times daily until a single candidate garners enough support - at which point the smoke coming from the Sistine Chapel chimney will be white.
After celebrating Mass this morning, they returned to the Sistine Chapel to resume voting.
They can vote twice in the morning. If those ballots are inconclusive, black smoke will once again rise from the chimney and the election will resume after lunch.
Voting takes place in silence, with no formal debate, until a decision is reached. If that does not happen after three days, there may be a pause for prayer and informal discussion for a maximum of one day.'Bereft'
Crowds who had braved rain and storms to watch the cardinals go into the conclave on big screens in St Peter's Square cheered as the black smoke appeared at 19:41 (18:41 GMT) on Tuesday.
Conclave interactive video
Step inside our virtual Sistine Chapel as Philippa Thomas explains the process to elect a new Pope
"I thought it was going to be white, because they were late. I thought it was going to be white, but I was wrong," said Paolo Paparini, a 76-year-old man waiting faithfully amongst the crowd told the Associated Press news agency.
"Without a Pope I feel bereft, like an orphan. I pray to give the cardinals the strength to choose the right man to lead the Church," French priest Guillaume Le Floch told the Agence France-Presse news agency.
"It cannot be an easy decision, but the Church needs a great leader now more than ever. The cardinals have a chance to astonish us," he said.
At one point feminist activists from the Ukrainian Femen group set off flares of pink smoke in the square to highlight what their website calls "the bloody violent history of Christianity" and the group's "determination to combat sexism of religion".
The topless protesters were dragged away by police.
The buzz in Rome is that a new Pope may be elected by Friday night, perhaps even earlier, says the BBC's David Willey who is there.
There is no desire among the cardinals for a prolonged conclave, he says.
From now on the cardinals - all under 80, as those over 80 are excluded - will eat, vote and sleep in closed-off areas until a new Pope is chosen.
Jamming devices in the Sistine Chapel should block all electronic communication and anyone tweeting would in any case risk being excommunicated.
