I heard this in the news today and searched the net. This is what came up on top:

http://www.telegraph.co.uk/news/2017/09/11/bones-attributed-st-peter-found-chance-1000-year-old-church/

Bones attributed to St Peter found by chance in 1,000-year-old church in Rome

The bones were found in clay pots in the historic church of Santa Maria in Cappella CREDIT: CODICE/RAI UNO

• Nick Squires, rome

11 SEPTEMBER 2017 • 3:50PM
Bones attributed to St Peter have been found by chance in a church in Rome during routine restoration work, 2,000 years after the apostle’s death.
The relics of the saint, who is regarded as the first Pope, were found in clay pots in the 1,000-year-old Church of Santa Maria in Cappella in the district of Trastevere, a medieval warren of cobbled lanes on the banks of the Tiber River.
The bones were discovered when a worker lifted up a large marble slab near the medieval altar of the church, which has been closed to the public for 35 years because of structural problems.







It had long been hoped the bones would one day be found in the 1,000-year-old church CREDIT: CODICE/RAI UNO
The workman immediately notified the deacon of the church, Massimiliano Floridi. “There were two clay pots which were inscribed with the names of early popes – Peter, Felix, Callixtus and Cornelius. I’m not an archaeologist but I understood immediately that they were very old,” he told Rai Uno, an Italian television channel. “Looking at them, I felt very emotional.”

It had been known for centuries that the relics might exist – they are recorded on a stone inscription in the church, which claimed they were kept alongside a fragment of a dress worn by the Blessed Virgin.  But until now, the relics had never been found.


The bones were discovered when a worker lifted up a large marble slab near the medieval altar of the church CREDIT:CODICE/RAI UNO
The remains have been handed to the Vatican for further study. Without proper analysis, it is impossible to say whether they belong to St Peter. “We’re waiting for a detailed study to be undertaken,” said the deacon. “A DNA comparison between these bones and those kept by the Vatican would shed light on the issue.”
A Vatican spokesman said it was too early to comment on the discovery.


A stone inscription in the church records the fact that it guards the relics of St Peter and other early popes, as well as martyrs CREDIT: CODICE/RAI UNO
It is not yet known how or why the relics came to be interred in the Church of Santa Maria in Cappella, which was consecrated in 1090.
One theory is that they were transferred there from the Vatican by Pope Urban II at a time of schism within the Catholic Church.
While Urban was generally recognised as the legitimate pope, he faced a challenge from an anti-pope, Clement III, who had set up a rival power base in Rome, backed by the Holy Roman Emperor Henry IV.  The church in Trastevere was closely linked to Pope Urban and may have been seen by him as a secure place in which to hide the bones.


The name of St Peter is inscribed on the lid of the clay potCREDIT: CODICE/RAI UNO
Conventional wisdom has it that St Peter was crucified, upside down, in Rome in the first century AD.

His remains were interred in a tomb on the Vatican Hill, where the Emperor Constantine later built a church, which in the 16th century was replaced by the current imposing basilica.
During excavations under St Peter’s Basilica that began after the Second World War, archaeologists discovered a funerary monument with a casket built in honour of Peter and an engraving in Greek that read "Petros eni", or "Peter is here".


The remains of St Peter are said to be buried beneath St Peter's Basilica CREDIT: GETTY
The remains were forensically examined in the 1960s, with experts concluding that they belonged to a man in his early sixties who lived in the first century AD. That was proof enough for Pope Paul VI, in 1968, to declare them the bones of St Peter.
During a Mass in 2013, Pope Francis publicly unveiled the bone fragments, reviving the debate over whether they really belong to the first pope. It was the first time the nine pieces of bone, encased in a box inside a bronze display case, had ever been exhibited in public.
Federico Lombardi, the then Vatican spokesman, said there was a “serious possibility” that the bones were from St Peter, “but we don't go beyond that".

S. Peter's bones or not this means something very significant, I just don't know what it is.

Indeed, I don't know what to make of it either, but it is certainly captivating that it is possibly 4 different Pope's all in one spot. I hope they actually tell us the results of the DNA test, if they ever do it.

S. Peter's bones or not this means something very significant, I just don't know what it is.

It means once again to all man made religions (Protestants) that the Catholic church is the one that has existed back in the day of the apostles, not "them" that was founded by a man, not God.  
However having said this it has always been my understanding that St.Peter (first Pope) was buried in Rome and the Church knows exactly where.  If I recall, under an altar?  Anyone help!

The bones were found years ago, in the 1930s before the beginning of the Crisis, in an area under the main altar of Saint Peter's Basilica.  They were not found directly under the main altar, but that is explained as the early Christians did not want to absolutely identify the location of the saint's grave lest they be defiled by the Pagans of the age.  All evidence is that these were, indeed, the bones of Saint Peter.  Only the Modernists have doubts.

The entire story is recounted in a book entitled, The Bones of St. Peter.  I don't know who wrote the book as I got it through the local public library and don't have a copy.

Interesting, but suppose parts of bones could be found in other locations? It is not uncommon for Saints to have the major parts of the skeleton in one place and pieces of other bones elsewhere. I suppose that it certainly could be possible. A good example of this would be St. Philomena, who's skeleton is housed in a statue in Italy but also has other bones and fragments in reliquaries around the world. We even have a reliquary with what I think is a piece of bone here in Houston. It's at Queen of Angels (SSPX) in Dickenson, which the church used to be famouse for.

(From memory.)  
I think the skull is NOT with the bones beneath St. Peter's Basilica and this was not a surprise when they were discovered, as the skull of St. Peter is preserved elsewhere. (If I remember correctly.) I read about this years ago and the archaeology behind it is sound. St. Peter was buried in a small grave next to a wall in the cemetery on the Vatican Hill. If you crossed the Tiber and headed up the hill on the road, or street that was there, to your left would have been an amphitheater which Caligula had built, and to your right was a cemetery, and farther up the Hill were gardens owned by the Imperial family. St. Peter was crucified in that amphitheater. Christians were burned to death like living torches in those gardens.  
When Constantine built his basilica, he had a large part of the hill excavated (I think he carried three baskets of dirt in the operation himself) and that cemetery was buried. The one wall of the amphitheater became one of the foundations for the new basilica, its "left" side,as it were. The altar was built over where St. Peter was buried. They had a steps going down to the site.  
When they built the new basilica in the 1500s, they did not make the grave accessible any longer.  The steps under the altar went down to a chapel over the site, but you couldn't get to it anymore. 
What happened in the 30s was there was an excavation beneath the basilica and they excavated the old cemetery. When they got to the spot beneath the altar, they found the old wall. There were no bones in the grave except animal bones. (not uncommon.) There was a niche in the wall in which they found the skeleton, without the skull. ther was an inscription in the general area also that read "Peter is here." After studying the bones, they concluded it was St. Peter.  
The skull was missing because at some point it was deliberately taken to another church (I forget which one) in the days of the first basilica. 
As to why the bones were in the wall, this is the theory: During a Saracen invasion of the city (900s?) the bones of BOTH Peter and Paul (and perhaps others) were taken OUT of their graves and hidden somewhere for safe keeping.  After the crisis, they were RETURNED. The theory is that at this time they put Peter in the wall. That may or may not be correct.  We know from the work done just the other year that Paul was put back in his place. Like Peter, his tomb was later made inaccessible (that was probably in the 1800s when St. Paul's burned down and had to be rebuilt.)
So, having said all that, I would guess that these are some relics of the early popes that were put in this church sometime between the 300s and the construction of the current basilica.  

Here, this is much better than what I scribbled up there. They have a little video on it that shows the grave site up until the first basilica was built. That's a little different than I remember reading -- it seems the wall was not there yet when Peter was buried. They must have come to the conclusion that the spot was built up after Peter was already buried. It doesn't make a big difference materially. (This article does not go into the question of moving bones around. It is just about the site beneath St. Peter's)

There is something I forgot to mention, that always fascinates me. The obelisk in St. Peter's Square was standing in that amphitheater. Caligula had it brought from Egypt. It was moved from the old site, to its current location sometime -- I guess -- in the 1500s, or 1600s.  The thing that gets me about it is that it is one of the last things St. Peter, the historical man Simon Peter Bar Jona, would have seen. It was there, towering over the man as he hung upside down dying on the cross, like some kind of sentinel.


http://www.culturaltravelguide.com/real-tomb-saint-peter-under-saint-peters-basilica