Pope John Paul II, the first Slav pope in history, is already being called a future saint.
He has been buried in a crypt under St Peter's Basilica a few metres from the reputed tomb of the first pope, the apostle Peter. But will he remain there?
The tomb of St Peter is the holiest of the Vatican shrines
The Vatican takes its name from a hill - not one of the seven hills of Rome, incidentally - called the Mons Vaticanus.
The emperor Nero built a track for chariot races there, next to a pagan cemetery.
This area under the basilica was excavated by archaeologists during the mid-20th Century when it was announced with a fanfare of publicity that the original tomb of St Peter, venerated there for nearly two millennia, had finally been located.
You can visit this Roman burial ground - there is a street full of tombs, not many of them Christian.
It is an eerie experience to find yourself in a small underground city street complete with pavements and brick buildings dating back at least 1,700 years.
It is difficult to figure out the details for yourself. Like most archaeological sites it all looks a bit of a damp and dusty jumble of brick and stone, but the graphic evidence is there that from very early times St Peter was venerated here.
You can see ancient graffiti invoking both Peter and Paul.
You emerge from the excavations into a second level of underground chambers which are gleaming with newly polished marble.
Here are a series of chapels which show how the first Slav pope has given new prominence in the crypt of St Peter's to the saints of eastern Europe.
There is a newly refurbished Polish chapel, one dedicated to the Hungarians, another to the Czechs, another to St Cyril and St Methodius, declared patron saints of all Europe by Pope John Paul.
It was Cyril who is credited with having invented the Cyrillic alphabet used in many Slav countries.
Pilgrims come and pray by the tombs of a host of popes
I asked the custodian Vittorio about the tiny chapel where Pope John Paul II has chosen to be buried.
"You see there," he pointed. "That's where the good Pope John XXIII used to lie until they carried him upstairs."
The mummified remains of Pope John - who was promoted by Pope John Paul II to the ranks of a blessed, the prelude to a declaration of full sainthood - now lie in a crystal reliquary under an altar in the main body of the basilica.
Catholics of many nationalities come every day to pray at his tomb.
"John Paul used to come down here to pray in the crypt where all his recent predecessors are buried at the end of each of his foreign journeys.
"He used to come alone, very early in the morning," Vittorio told me.
"They say he wrote in his will he wanted to be buried in Poland, but I know he wanted to lie here."
Final resting place?
Up to a million Poles, maybe even more, no-one is very sure, have come to Rome to attend the funeral of the man who is their national hero as well as the Pope of Rome.
Many have pleaded that the Pope's body, or at least his heart, should be returned to his native land for burial.
The labyrinthine crypt under the Vatican holds many tombs
But that would not be possible at the moment, as the late Bishop of Rome wanted to make his final resting place, here, in naked earth, marked by a simple slab, not one of those elaborate marble tombs of which Roman churches boast so many examples.
Of course, John Paul's body could always be moved at some time in the future.
The remains of the Borgia pope from Spain, who ruled here at the beginning of the 16th Century, have long ago been removed to Spain.
But the tomb here of Pope Hadrian IV, the first and only English pope - whose real name was Nicholas Breakspear - never found its way back north of the Alps and is still down here in the crypt.
So is the tomb of the only woman to share the honour of burial with the popes - the former Protestant monarch Queen Christina of Sweden, who famously gave up her throne, converted to Catholicism, and came to live in Rome.
After the pomp and circumstance of the biggest papal funeral in history, in terms of the attendance of heads of state and government, the sheer number of mourners and the number of people around the world who will be watching it on television or listening on the radio, Pope John Paul has chosen to be buried in the simplest way.
Two popes died in 1978, when thousands prayed at the tombs
He has fulfilled his desire to be near as possible to the place where Peter, the first pope, is believed to lie.
I will hazard a guess that very shortly his tomb will become one of the most visited shrines in the Catholic world.
From Our Own Correspondent was broadcast on Thursday, 7 April, 2005, at 1100 BST on BBC Radio 4. Please check the programme schedules for World Service transmission times.