  We study transport in a smooth random magnetic field, with emphasis on
composite fermions (CF) near half-filling of the Landau level. When either the
amplitude of the magnetic field fluctuations or its mean value $\bar B$ is
large enough, the transport is of percolating nature. While at $\bar{B}=0$ the
percolation effects enhance the conductivity $\sigma_{xx}$, increasing $\bar B$
(which corresponds to moving away from half-filling for the CF problem) leads
to a sharp falloff of $\sigma_{xx}$ and, consequently, to the quantum
localization of CFs. We demonstrate that the localization is a crucial factor
in the interplay between the Shubnikov-de Haas and quantum Hall oscillations,
and point out that the latter are dominant in the CF metal.
