I believe that voxel cone tracing is state of the art if you want to do real time GI. I think Crytek and Unreal 4 have it, though I'm not sure if anybody's shipped an actual game with it yet.
In terms of slightly more feasible technology, a lot of people are using prebaked SH environment probe based approaches. Essentially, set up environment probes as usual, compute SH to however many terms you feel like having, and save them off. Interpolate at runtime between nearby probes with whatever clever hacks you feel like applying and create a lighting environment like that.