Was the apostle Peter martyred in Rome? There are some legends that say that Peter traveled to Rome where he was martyred.

Is this legend true? Are there any historical accounts that support the legend? Are there any other theories about the later life of apostle Peter? Is there any historical evidence that he was bishop of Rome?
It is generally accepted that Peter was crucified upside down in Rome.  Tertullian and Origen attest to this.

From WikiPedia:


  According to the 1911 Catholic Encyclopedia, St. Peter labored in Rome
  during the last portion of his life, and there ended his life by
  martyrdom.[17] The death of St. Peter is attested to by Tertullian at
  the end of the 2nd century, and by Origen in Eusebius, Church History
  III.1. Origen says: "Peter was crucified at Rome with his head
  downwards, as he himself had desired to suffer."[17] This is why an
  upside down cross is generally accepted as a symbol of Peter, who
  would not have considered himself worthy enough to die the same way as
  his Savior.[35]


Whether or not Peter was bishop of Rome is still debated, although it is a belief held by the Catholic church.