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The Eleventh Doctor, River Song and Amy Pond witnessed the Byzantium crash on Alfava Metraxis during the 51st century. It carried a Weeping Angel and when the ship crashed, the Angel was let loose. (TV: The Time of Angels) It transpired that the Angel had sabotaged the ship and forced it to crash, so its starving brethren on the planet could feed off the ship's energy. Once crashed, the ship began to emit radiation from its drives, harmful to humans but a source of food for the Weeping Angels.
The Byzantium could travel for ten years between planetfalls, partially due to it having an enormous forest within itself, with modified trees to convert starlight into oxygen for the crew to breathe. (TV: Flesh and Stone)
After the Byzantium crashed, its home box eventually ended up in the Delirium Archive in the 171st century, where the Doctor and Amy found it and used the information contained on to pilot the TARDIS to it, catching River as she escaped through an airlock into space. (TV: The Time of Angels)
While at Stonehenge, Amy recalled River Song telling the Doctor after the crash of the Byzantium that she would see them again when the Pandorica opens. However, this River was earlier in her timeline and while River acknowledged she would do so, she hadn't yet. (TV: The Pandorica Opens)
When River met the Tenth Doctor in the Library in the 51st century shortly before her death, she mentioned the crash of the Byzantium from her diary, saying it was in his "early days" as it clearly wasn't "ringing any bells" . (TV: Silence in the Library)