  In this review, we show how advances in the theory of magnetic
pseudodifferential operators (magnetic $\Psi$DO) can be put to good use in
space-adiabatic perturbation theory (SAPT). As a particular example, we extend
results of [PST03] to a more general class of magnetic fields: we consider a
single particle moving in a periodic potential which is subjectd to a weak and
slowly-varying electromagnetic field. In addition to the semiclassical
parameter $\eps \ll 1$ which quantifies the separation of spatial scales, we
explore the influence of additional parameters that allow us to selectively
switch off the magnetic field.
  We find that even in the case of magnetic fields with components in
$C_b^{\infty}(\R^d)$, e. g. for constant magnetic fields, the results of
Panati, Spohn and Teufel hold, i.e. to each isolated family of Bloch bands,
there exists an associated almost invariant subspace of $L^2(\R^d)$ and an
effective hamiltonian which generates the dynamics within this almost invariant
subspace. In case of an isolated non-degenerate Bloch band, the full quantum
dynamics can be approximated by the hamiltonian flow associated to the
semiclassical equations of motion found in [PST03].
