  Both brane tilings and exceptional collections are useful tools for
describing the low energy gauge theory on a stack of D3-branes probing a
Calabi-Yau singularity. We provide a dictionary that translates between these
two heretofore unconnected languages. Given a brane tiling, we compute an
exceptional collection of line bundles associated to the base of the
non-compact Calabi-Yau threefold. Given an exceptional collection, we derive
the periodic quiver of the gauge theory which is the graph theoretic dual of
the brane tiling. Our results give new insight to the construction of quiver
theories and their relation to geometry.
