  We review the current understanding of the uniform two-dimensional (2D) Fermi
gas with short-range interactions. We first outline the basics of two-body
scattering in 2D, including a discussion of how such a 2D system may be
realized in practice using an anisotropic confining potential. We then discuss
the thermodynamic and dynamical properties of 2D Fermi gases, which cold-atom
experiments have only just begun to explore. Of particular interest are the
different pairing regimes as the interparticle attraction is varied; the
superfluid transition and associated finite-temperature phenomenology; few-body
properties and their impact on the many-body system; the Fermi polaron problem;
and the symmetries underlying the collective modes. Where possible, we include
the contributions from 2D experiment. An underlying theme throughout is the
effect of the quasi-2D geometry, which we view as an added richness to the
problem rather than an unwanted complication.
