  This is a review paper concerned with the global consistency of the quantum
dynamics of non-commutative systems. Our point of departure is the theory of
constrained systems, since it provides a unified description of the classical
and quantum dynamics for the models under investigation. We then elaborate on
recently reported results concerned with the sufficient conditions for the
existence of the Born series and unitarity and turn, afterwards, into analyzing
the functional quantization of non-commutative systems. The compatibility
between the operator and the functional approaches is established in full
generality. The intricacies arising in connection with the explicit computation
of path integrals, for the systems under scrutiny, is illustrated by presenting
the detailed calculation of the Feynman kernel for the non-commutative two
dimensional harmonic oscillator.
