  Two types of commensurability effects are possible in a large Josephson
junction patterned with columnar defects. The first occurs for a periodic array
of pins when the mean fluxon spacing (tuned by the magnitude of the applied
in--plane magnetic field) is a rational fraction of the defect spacing. We show
that this effect leads, under fairly general conditions, to a mapping of the
behavior of the Josephson junction near the commensurate field values to that
of a zero field junction with an effective Josephson penetration depth. The
second occurs for more general arrangements of pinning sites, when the
orientation of the Josephson vortex lattice (tuned by the direction of the
applied field) nearly matches the orientation of the defects. We investigate
this tilt response in the limit of a single Josephson vortex. The results are
compared, where possible, to recent experiments. As an aside from our main
analysis, we prove that, contrary to recent claims in the literature, the
critical current density vanishes in the thermodynamic limit, even in the
presence of (non--pathologically distributed) pinning disorder
