If you're just now getting into the story of Final Fantasy XIII and its sequels, it might be quite a task to go through both the first and second game, just to be caught up for Lightning Returns.
Square Enix put together an awesome video that recaps the story of both Final Fantasy XIII and XIII-2 in awesome-tacular 16-bit fashion, making it look like it was made right during the SNES era.
Of course, you're getting the condensed story here, for the full experience, you should definitely play through both games (I'll openly admit I enjoyed them, despite the hate they received).
Lightning Returns: Final Fantasy XIII will be coming to Xbox 360 and PlayStation 3 on February 11 in the US, and February 14 in Europe.
