  We describe quantum and classical Hamiltonian dynamics in a common Hilbert
space framework, that allows the treatment of mixed quantum-classical systems.
The analysis of some examples illustrates the possibility of entanglement
between classical and quantum systems. We give a summary of the main tools of
Berezin-Toeplitz and geometric quantization, that provide a relation between
the classical and the quantum models, based essentially on the selection of a
subspace of the classical Hilbert space. Coherent states provide a systematic
tool for the inverse process, called dequantization, that associates a
classical Hamiltonian system to a given quantum dynamics through the choice of
a complete set of coherent states.
