  We prove quantization of the Hall conductance for continuous ergodic Landau
Hamiltonians under a condition on the decay of the Fermi projections. This
condition and continuity of the integrated density of states are shown to imply
continuity of the Hall conductance. In addition, we prove the existence of
delocalization near each Landau level for these two-dimensional Hamiltonians.
More precisely, we prove that for some ergodic Landau Hamiltonians there exists
an energy $E$ near each Landau level where a ``localization length'' diverges.
For the Anderson-Landau Hamiltonian we also obtain a transition between
dynamical localization and dynamical delocalization in the Landau bands, with a
minimal rate of transport, even in cases when the spectral gaps are closed.
