  We review recent results obtained within the framework of the integer quantum
Hall effect in the spirit of the work of Germinet, Klein, Schenker in
\cite{GKS}. Landau Hamiltonians perturbed by random electric or magnetic
perturbations are shown to exhibit a dynamical mobility edge, that is a
transition between a regime of dynamical localization and a regime of non
trivial transport at a minimal rate. The focus is put on three situations of
interest: 1) unbounded ergodic electric potentials, for which Landau gaps are
filled; 2) non ergodic electric potentials; 3) random magnetic potentials.
