There are several papal contenders waiting in the wings, but no obvious front-runner - as was the case when Pope Benedict was elected pontiff in 2005 after the death of Pope John Paul II.
Here are the main contenders:
Cardinal Francis Arinze -odds 15/8
Born in Nigeria, 1932, the 80-year-old would be the first African in 1,500 years to sit on the throne of St Peter.
He was baptised on his ninth birthday after converting.
He was educated at Urban University in Rome and earned a post-graduate qualification from London University.
Cardinal Arinze was ordained in 1958 and became the world's youngest bishop, aged 32, in 1965. He was created cardinal in 1985.
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Cardinal Peter Turkson - odds 9/4
Considerably younger than his rivals, the Ghanian is the current President of the Pontifical Council for Justice and Peace.
Born to a Methodist mother and a Catholic father in 1948, he became a priest in 1975.
The 64-year-old speaks Fante, English, French, Italian, German, Hebrew, Aramaic, Arabic and Greek.
Head of the Vatican justice and peace bureau, he is spokesman for the Church's social conscience and backs world financial reform.
He was named Cardinal in 2003 and would be the first African to become Pope in 1,500 years.
Cardinal Marc Ouellet - odds 5/1
The 68-year-old was born in Canada in 1944. He became the archbishop of Quebec in 2002 and was created cardinal in 2003.
He once said becoming Pope "would be a nightmare."
He is currently head of the Vatican office that oversees the appointment of the world's bishops.
Cardinal Angelo Scola - odds 7/1
The Italian Cardinal was born in 1941. He studied philosophy at the Catholic University of Milan and was ordained to the priesthood in 1970.
The 71-year-old was created cardinal in 2003.
He worked with Pope Benedict XVI on the theological journal 'Communio' and is a long-time ally of the Pope.
Odds provided by Paddy Power.
[Related: Pope Benedict resigns: Full text of his declaration]
The others in the running:
Cardinal Timothy Dolan
The 62 year-old, from the USA, became the voice of U.S. Catholicism after being named archbishop of New York in 2009.
His humour and dynamism have impressed the Vatican, where both are often missing. But cardinals are wary of a "superpower pope" and his back-slapping style may be too American for some.
Cardinal Gianfranco Ravasi
The Italian has been Vatican culture minister since 2007 and represents the Church to the worlds of art, science, culture and even to atheists.
This profile could hurt the 70-year-old if cardinals decide they need an experienced pastor rather than another professor as Pope.
[Related: Pope Benedict resigns: Charming and shy, the man who tamed the 'Rottweiler image']
Cardian Odilo Pedro Scherer
The Brazilian, 63, ranks as Latin America's strongest candidate. Archbishop of Sao Paolo, largest diocese in the largest Catholic country, he is conservative in his country but would rank as a moderate elsewhere.
The Roman Catholic Church could look away from Europe for its new leader and turn to Latin America, where 42% of the world's 1.2 billion-strong Catholic population come from.
Cardinal Christoph Schoenborn
Cardinal Schoenborn is a former student of Pope Benedict with a pastoral touch the pontiff lacks. The Austrian Cardinal, 67, has ranked as papal material since editing the Church catechism in the 1990s.
But some cautious reform stands and strong dissent by some Austrian priests could hurt him.
Cardinal Angelo Scola
The 71-year-old is archbishop of Milan, a springboard to the papacy, and is many Italians' bet to win.
An expert on bioethics, he also knows Islam as head of a foundation to promote Muslim-Christian understanding. His dense oratory could put off cardinals seeking a charismatic communicator.
Cardinal Luis Tagle
The only Asian candidate in the running, Cardinal Tagle, 55, has a charisma often compared to that of the late Pope John Paul.
The Filipino is also close to Pope Benedict after working with him at the International Theological Commission. While he has many fans, he only became a cardinal in 2012 and conclaves are wary of young candidates.