  In a series of papers we have argued that the 'basic' physical procedure of
minimal coupling giving the quantum description of a Hamiltonian system
interacting with a magnetic field, can be given a very satisfactory
mathematical formulation as a twisted Weyl quantization \cite{MP2}. In this
paper we shall present a review of some of these results with some modified
proofs that allow a special focus on the dependence on the behavior of the
magnetic field, having in view possible developments towards problems with
unbounded magnetic fields. The main new result is contained in Theorem 2.9 and
states that the the symbol of the evolution group of the self-adjoint operator
defined by a real elliptic symbol of strictly positive order in a smooth
bounded magnetic field is in the associated magnetic Moyal algebra, i.e. leaves
invariant the space of Schwartz test functions and its dual
