Dr. Leik Myrabo from RPI is one of the main pushers behind this. When I was taking his classes back in the 80's I was impressed with the idea but somewhat dubious of its practicality. However, he has done some pretty impressive experiments and it could be practical in a few decades.
Do a google for his name and you will find lots of info; fortunately it googles well as it's a bit more distinctive than John Smith for example.
As I recall, the biggest obstacles to making this practical are:
1. Laser power
2. High temp materials
3. Optics able to handle the high power densities required
4. I'm sure there's more but those occur straight away
The experiments he's run to date are sort of brute force using the laser to cause detonation of the air itself. His concept is to use this for initial boost and then after sufficient velocity is attained(M 5-8 IIRC) transition to what he calls an MHD fanjet powered by a ground or space based laser.
He's written several books on the subject and I don't even know how many papers. If you're really interested then shoot him an e-mail - he'll certainly cover you up with info as he's a bit the crusader type when it comes to this.