The gospels point to different sources of initial concern among the Jewish authorities. Mark suggests that the Jewish authorities were concerned primarily with the confrontation Jesus had with traders in the Temple, while Luke's account identifies their primary concern as his teachings in the Temple. John, meanwhile, points to a fear among Jewish authorities that Jesus' rising popularity could lead to an uprising that would provoke a violent response from Rome.
All four Biblical accounts agree, however, that Caiaphas and the Sanhedrin ultimately condemned Jesus for blasphemy. The gospels record that when Caiaphas asked Jesus whether he claimed to be the Messiah, he replied, "I am" (Mark 14:62) (or "You have said so" (Matthew 26:64) or "If I tell you, you will not believe" (Luke 22:67-8) or "You say that I am" (John 19:7)). Although the Mishnah, the Jewish lawcode assembled around 200 C.E., defined blasphemy more narrowly as speaking the sacred name of God (YHWH), the gospel writers suggest a looser first-century construction of the term, one that includes a variety of serious theological offenses.
After his condemnation by Jewish authorities, Jesus was brought--under all but Peter's account--to the Roman prefect of Judea, Pontius Pilate. The reason, according to John, was that the death penalty was not an available option for the Sanhedrin under Roman law. (It should be noted, however, that the Sanhedrin operated during these times with less than complete independence to implement Jewish law, having a dual political and religious status.) There is, however, strong reason to believe that Jewish authorities could, had they so desired, executed Jesus. The well-substantiated executions--by stoning--of two first-century Christians, Jesus's brother James in 62 C.E. and Stephen show that capital punishment was--at least within a few decades of Jesus' trial--practiced by Jewish authorities. Moreover, Temple inscriptions from the period warn of death to Gentiles that pass into certain restricted areas.
Biblical accounts of the trial before Pilate are largely fictional, according to most scholars. It is unlikely that any supporter of Christ would have been in a position to record any questioning of Jesus by Pilate that might have taken place.
Whatever their basis, the gospels portray a Pilate initially unpersuaded of Jesus' guilt. For example, in Mark, after Pilate asks Jesus about "the many charges [the chief priests] bring against you," Jesus makes "no further answer" and "Pilate wondered." Later, Mark reinforces his suggestion of a reluctant executioner when he writes, "For [Pilate] perceived that it was out of envy that the chief priests had delivered him up." Finally, Mark makes Pilate's doubts explicit by having him almost beg the crowd to release Jesus over the (almost certainly invented) prisoner Barabbas. Pilate asks the crowd there thirst for the blood of Jesus: "Why, what evil has he done?" Pilate allows the crucifixion of Jesus, in the gospel accounts, not out of a conviction that Jesus did anything wrong, but only to "satisfy the crowd." If there were still any doubt about Pilate's doubt, the gospels report that after authorizing his execution, he "washes his hands."
The gospel accounts so transparently attempt to present the chief priests--and not Pilate--as the more blameworthy party that scholars have raised numerous questions about their accuracy. Scholars have paid special attention to the incentives of Mark because he wrote the earliest of the four gospel accounts in the Bible, and Matthew, Luke, and (to a lesser extent) John based their accounts on his. The scholars point out that Mark--writing at a time of Roman prosecution of Christians and for a largely non-Jewish audience--had incentives to present a story that would minimize the risk of condemnation by Roman authorities and maximize his prospects for winning converts to Christianity from among the Romans in his audience. How could Mark, these scholars ask, possibly have known what Pilate "wondered" about Jesus' guilt or what he "perceived" about the purposes of high priests?