In reply to elliot.baker:
I can't comment on yoga because I've never really gotten into it properly but I can recommend some videos that show great exercises that have helped me.
For low body stretches I do this guys routine, which has massively improved my flexibility and footwork - I particularly recommend working on hip flexibility if you are lacking in that area, as it will allow you to unlock higher and further foot holds.
https://www.youtube.com/watch?v=wDqmtJs4WvA&t=777s
For core I do a similar routine like this that you can do in any climbing gym, any TRX exercises I've found are very effective too, I think generic core exercises like planks are great too when you really can't hold on to anything any more, though painfully boring, but in general I try to do movements that emulate climbing forces where possible:
Injury prevention for me includes working out the opposing muscles to the muscle you usually use in climbing, These are general upper body stretching, and general 'pushing' exercises such as dips, pushups, and shoulder presses.