The texture files of the model have to be imported into Unity as well. The materials of the model are probably there after the import, but they probably need the textures hooked up to them. You also have to choose which shader to apply to the material.
If you’re using humanoid models, I’ve found the rigging to be a real problem. For Mecanim, at least, the rig has to be done just the way Mecanim wants it. If you’re bones aren’t setup just the way it likes you’ve got major problems. I resorted to skinning and rigging the models over again from scratch using the exact bone structure Mecanim wants, which worked quite well using the Humanoid option. Hope that helps some how.
But if it’s not animating and its not a problem with the animation, then I would expect the rigging in Unity.