  We present a consistent framework of coupled classical and quantum dynamics.
Our result allows us to overcome severe limitations of previous
phenomenological approaches, like evolutions that do not preserve the
positivity of quantum states or that allow to activate quantum nonlocality for
superluminal signaling. A `hybrid' quantum-classical density is introduced and
its evolution equation derived. The implications and applications of our result
are numerous: it incorporates the back-reaction of quantum on classical
variables, it resolves fundamental problems encountered in standard mean field
theories, and remarkably, also the quantum measurement process, i.e. the most
controversial example of quantum-classical interaction is consistently
described within our approach, leading to a theory of dynamical collapse.
