Libertarianism is a political philosophy advocating that individuals should be free to do whatever they wish with their person or property, as long as they do not infringe on the same liberty of others.
Hmm. Nice idea. Too bad it doesn't work, right out of the gate.
See there are too many places (especially in the Gap) where there's no authority in place to keep such infringements from happening. Libertarian non-interventionism is ok for me if I've got some structure to protect my person and property, but I won't do anything to help you, in, say, Sudan, build such a structure.
As to the critiques, I tend to be sympathetic to those from the left and the right, which I would frame as 'markets need some regulation' and 'we have some of those traditions because they're good for us'.
Anyway, how's that for a start? ;-)