  This survey offers a systematic and streamlined exposition of the most
important characterizations of Gabor frames over a lattice. The goal is to
collect the most important characterizations of Gabor frames and offer a
systematic exposition of these structures. In the center of these
characterizations is the duality theorem for Gabor frames. Most
characterizations within the $L^2$-theory follow directly from this fundamental
duality. In particular, the celebrated characterizations of Janssen and
Ron-Shen are consequences of the duality theorem, and the characterization of
Zeevi and Zibulski for rational lattices also becomes a corollary. The novelty
is the streamlined sequence of proofs, so that most of the structure theory of
Gabor frames fits into a single, short article. The only prerequisite is the
thorough mastery of the Poisson summation formula and some basic facts about
frames and Riesz sequences.
