The chimney has been erected above the Sistine Chapel
Roman Catholic cardinals from 52 nations around the world are preparing to elect a successor to Pope John Paul II, who died on 2 April.
The BBC News website looks at the key stages of the process and the rituals involved, some of which have been repeated down the centuries.
What is a conclave?
It is a meeting of cardinals held to select a pope. The term comes from the Latin phrase cum clavi "with a key", because the cardinals used to be "locked away" in the Sistine Chapel until they reached a decision.
Entrances were sealed and curtains closed. The cardinals even slept in the chapel.
Pope John Paul II had a hotel residence built for them instead. But they still are not allowed to leave the Vatican.
Where is it being held?
After a morning mass in St Peter's Basilica, the cardinals moved in procession to a guarded annex of the Sistine Chapel, where they will have sworn an oath of secrecy.
The annex will have been screened for bugging devices.
The cardinals have no access to telephones, radio or television, until it is all over, and may not talk to the media.
How many ballots are there?
On the first afternoon of the conclave, cardinals have the option of holding an initial ballot. This would give them an opportunity to gauge the level of support for various candidates.
However, the normal practice is to begin voting the following morning. From this point on, there will be four ballots a day - two in the morning and two in the afternoon - until a new pope is chosen.
How is the voting conducted?
Cardinals write their choice on a ballot paper, taking care to disguise their handwriting.
Then they fold the papers, hold them up for all to see, and proceed to the altar, where there is a large chalice - the goblet used to hold wine during the service, and a paten - the shallow metal plate used to hold communion wafers during mass. Each cardinal puts his ballot paper in the paten and slides it into the chalice.
The votes are counted by randomly selected cardinals.
Why do people watch for smoke coming from the chapel?
The ballot papers are burned in a stove after every second vote - at around midday and in the late afternoon or early evening. The smoke from the stove comes out of a special chimney, a rust-coloured pipe erected on top of the chapel in the days before the conclave starts.
Black smoke indicates no decision has been made. White smoke signals a successful election.
How long does it all take?
Over the past century the election has taken anything from two to five days.
After a few days, the cardinals can agree to take a break, if it is proving difficult to reach the required two-thirds majority.
In 1996, John Paul II introduced changes that allow the election of a pope by a simple majority after about 30 unsuccessful ballots.
What happens when a pope is chosen?
When the cardinals reach their decision, each will lower a purple canopy over his chair, except for the elected pope. The final ballot papers are then burned, with the white smoke signalling a decision.
This time, the decision will also be signalled by the tolling of the bells of St Peter's Basilica, in case the smoke comes out grey (as it has sometimes in the past).
The Senior Deacon of the College of Cardinals, Jorge Cardinal Medina Estevez from Chile, asks the pope-elect if he accepts the decision and then steps out onto the balcony of the Vatican to shout: "Habemus Papam" ("We have a Pope!").
The new pope chooses the name by which he wishes to be called, dons his new robes and steps on to the balcony himself.
Where is the next pope likely to come from?
For 455 years before the election of Pope John Paul II, all popes had been Italian. One of the big questions now is whether Italy will get the papacy back.
Many Vatican watchers are doubtful, if only because the number of Italian cardinals has declined in recent years.
Much more likely, they believe, is that the next pope will be from the developing world - and most likely from Latin America, whose cardinals now form a powerful voting bloc. Nearly half of the world's baptised Catholics live in the Americas, and more live in Brazil than in any other country in the world.
There is also a chance that an African pope could emerge from the conclave.
Only 10 popes have been non-European and the last of these lived in the 8th Century. Two hundred and 11 popes have been Italian, about 86% of the total.