In Luke 23 we are told that over the course of Jesus' trial, Pilate sent Jesus to Herod [Antipas], and after questioning & mocking Jesus, Herod sent Jesus back to Pilate.
Then we are given this interesting historical aside:
12 And the same day Pilate and Herod were made friends together: for before they were at enmity between themselves.
vs. 15 further suggests Pilate considered Herod's judgement reliable. The text explains why Pilate sent Jesus to Herod (He was from Galilee which was ruled by Herod), but it is not so clear why these two leaders were at odds and then placated and what, if anything, that had to do with the trial.
Why was there enmity between Pilate and Herod in the first place?
In addition to the events of Luke 13:1-2 noted by Tony below, I also read this interesting article by Maier, who suggests (see pp. 11-12) that the "golden shields" incident (Pilate brought golden shields dedicated to Tiberius into Herod's palace in Jerusalem) may be a/the cause of strife between Pilate and Antipas.
Antipas joined the protest against the shields which ultimately led to Pilate being reprimanded by Emperor Tiberius. Maier dates this event to the Spring of 32; others have dated it somewhat earlier.
Pilate certainly had earned Antipas' antipathy.