Beam combined lasers might help with this problem too:
Oh... wait, aren't asteroids like little mini-planetoids? And wouldn't destroying one with satellite-based lasers using beam-combining technologies be sort of like blowing up a planet on a small scale? And, hmm, what would happen if, say, one aimed one of those things to the surface of the planet Earth...? Might this be why they're interested in figuring out this technology?