Usually the choices are chemical or abrasive. The abrasive methods such as the microblasters (
www.ccrco.com) can take off the coatings but usually removes any stenciling or printing on SMD boards as well. This is the favored method by those working on through-hole PCBs.
Chemical removers work well but have their own set of problems such as safety and disposal. They are usually less damaging than abrasive methods and work pretty good with SMD boards.
One of our military customers has some expensive automated laser-based removal system but I haven't located much information about it online.
For the thinner coatings sometimes simple alcohol is enough to soften it so it can be probed.
Here is a reasonably informative web page that I sometimes consult:
http://www.empf.org/empfasis/oct03/3403rcc.htm