If the leading names fail to reach the 77 votes required for victory in the first few rounds of balloting, any number of surprise names could come to the fore.
The first puffs of smoke from the Sistine Chapel chimney should emerge sometime around 8:00 pm local time (1900 GMT) on Tuesday.
Black smoke means "not yet" - the likely outcome after round 1 - meaning that voting will continue, with four rounds each day, until a pope is elected.
White smoke means the 266th pope has been chosen.
According to Vatican spokesman Father Thomas Rosica, there won't be much time between the election of the pontiff and the question of his new name being posed.
