  We study the dimensional crossover of weak localization in strongly
anisotropic systems. This crossover from three-dimensional behavior to an
effective lower dimensional system is triggered by increasing temperature if
the phase coherence length gets shorter than the lattice spacing $a$. A similar
effect occurs in a magnetic field if the magnetic length $L_m$ becomes shorter
than $a(D_{||}/D_\perp)^\gamma$, where $\D_{||}/D_\perp$ is the ratio of the
diffusion coefficients parallel and perpendicular to the planes or chains.
$\gamma$ depends on the direction of the magnetic field, e.g. $\gamma=1/4$ or
1/2 for a magnetic field parallel or perpendicular to the planes in a quasi
two-dimensional system. We show that even in the limit of large magnetic field,
weak localization is not fully suppressed in a lattice system. Experimental
implications are discussed in detail.
