I don't think the explosions were CG. I've never seen that done in an amateur video, where it's tracking the camera movements and with the smoke enveloping the actors. Anyways I would only believe it's CG if the producers of the film stated, and/or if someone here can prove me wrong by doing a similar feat.
EDIT:
Ok, that last one looked really impressive. Now I don't know what to think. Cool video and song though
EDIT 2:
Oh crap, it's directed by Spike Jonze? He's one of my favourite directors, and he doesn't shy away from technically complicated special effects and pyrotechnics. Don't you remember the intro to Jackass the movie? There were all these explosions on both sides of the shopping cart and shrapnel was flying in front and around them... I definitely think this is real now.
Also I love finding new awesome songs I've never heard before. This is M83 - Lower Your Eyelids to Die With the Sun in case anyone's wondering. Great song, great clip.