There is currently no easy way to have bones be controlled by a mesh. This severely limits rigging options when it comes to physics objects, or low poly meshes driving a rig that controls a high poly mesh.
It is possible to parent or constrain bones to vertices, but this is extremely time consuming, especially for complex rigs.
What would be very useful is a deform modifier style option to bind bones to nearby points of a mesh. This would give better options than are currently available with the deform modifier. At the moment, if you want to run a physics sim on a low poly mesh, your options are to use a deform modifier (which must be an enclosed cage, hugely limiting your options for the shape of the physics mesh) or spend hours setting up bone constraints that will take many more hours to adjust in the event of a change.