Born Melody Pond, to Amy Pond and Rory Williams during the Battle of Demon's Run, she was kidnapped by agents of The Silence and raised as the Doctor's perfect assassin. But in her pursuit of the Doctor, she fell in love with him, which broke her conditioning.
Becoming a Doctor of Archaeology, she was again recruited by The Silence to kill the Doctor at a fixed point in time. However, the assassination was staged to allow the Doctor to disappear from view. Handed 12,000 life sentences for his murder, River spent her days at Stormcage Containment Facility, but her nights travelling with the Doctor.
They investigated the wreck of the Byzantium, battled Weeping Angels in New York and visited the Singing Towers of Darillium. She died in The Library, saving the people trapped in its computer. The Doctor was able to upload her into the mainframe where her data ghost “lives” with three children to look after.
(The Doctor and River have met each other, broadly speaking, in reverse order - the first time the Doctor meets River is the last time she sees him.)