The motion of a quantum particle in a random magnetic flux in two dime
nsions is investigated. Two situations are distinguished, a ''Debye''
phase where the fluxes are uncorrelated, and a ''Meissner'' phase wher
e the fluxes-appear as neutral pairs. A geometrical interpretation of
effective single-particle action in these phases is emphasized. Result
s are discussed for (a) a continuum white-noise model where we employ
a trial-action method, (b) a continuum model with randomly distributed
flux tubes where we obtain the form of the Lifschitz tail, and (c) a
lattice model, where numerical results for the density of states and d
iamagnetic response of Debye and Meissner phases are given. An importa
nt conclusion is that the density of states in the Debye phase exhibit
s a sharp peak at an effective band edge.