The majority of the time, in Star Trek, when shields are used, they're used against energy weapons, such as phasers. We also know that shields block transport beams. They do keep out photon torpedoes, which are composed of a casing and a warhead.
It makes sense that shields would deflect energy (they are "deflector shields"). That would tell us how they work against phasers and why transport through shields wouldn't work. How do they work against physical objects? Do they deflect them? Are the objects disintegrated on contact? Do they work to prevent entry of certain types of matter and not others?