Among the figures who ensure continuity are the Vatican's number two Cardinal Angelo Sodano, Cardinal Joseph Ratzinger, in charge of church doctrine, and Archbishop Stanislaw Dziwisz, personal secretary to Pope John Paul II.
Then there is the Vatican's centuries-old bureaucracy, the Curia - a finely tuned machine that handles the Vatican's day-to-day operations.
In past centuries, popes sometimes delegated authority to Vatican officials who were nephews or other relatives.
Such nepotism is a thing of the past, and Sodano - whose role roughly corresponds to prime minister in a parliamentary democracy - has taken on an increasingly visible role since John Paul II was hospitalised with flu and breathing problems in February.
Ratzinger, who has been a guardian of the Pope's conservative policies on issues such as contraception and abortion, assumed other key responsibilities after the Pope fell ill.
And American Cardinal James Stafford presided over key Holy Week observances in the absence of the pontiff.
Behind the scenes, however, it is Dziwisz - a Pole like John Paul II - who has been the guardian of the pontiff's inner sanctum and the interpreter of his intentions. When the Pope was being treated at Rome's Gemelli Polyclinic hospital, it was Dziwisz who screened visitors.
Although as an archbishop he is lower in rank than the cardinals, he publicly berated Ratzinger in October 2003 after the cardinal was quoted in a German magazine as saying the Pope "was in a bad way" and that the faithful should pray for him.
"Cardinal Ratzinger was crying yesterday, explaining that he never gave an interview," Dziwisz said then.
Despite the powerful figures who run church affairs during papal health crises, ultimate authority on important decisions, such as the appointment of bishops or policy revisions, falls to the pontiff.
Even as he lay critically ill in his apartments at the Vatican on Friday, John Paul II appointed a large number of bishops and other church officials, the Holy See said in an afternoon statement.
Another set of officials takes over after a pope dies, including the camerlengo, or chamberlain, who administers the property and finances of the Holy See and organises the conclave to elect a new pope.