How to handle colliders in Unity3D?

I've tried virtually everything I can think of/read about online, but our character continues to be able to walk through any colliders we put on objects (except for floors). The character is stopped when it first touches an object, but if I keep on holding in the walk button, it manages to push it's way through. I've tried using mesh colliders and box colliders, making it check continuously etc. and nothing seems to work. Maybe it has something to do with the player's animation being made in Blender and imported into Unity? Any help would be appreciated.