  In this paper we propose a systematic construction of mirrors of nonabelian
two dimensional (2,2) supersymmetric gauge theories. Specifically, we propose a
construction of B-twisted Landau-Ginzburg orbifolds whose correlation functions
match those of A-twisted supersymmetric gauge theories, and whose critical loci
reproduce quantum cohomology and Coulomb branch relations in A-twisted gauge
theories, generalizing the Hori-Vafa mirror construction. We check this
proposal in a wide variety of examples. For instance, we construct mirrors
corresponding to Grassmannians and two-step flag manifolds, as well as complete
intersections therein, and explicitly check predictions for correlation
functions and quantum cohomology rings, as well as other properties. We also
consider mirrors to examples of gauge theories with U(k), U(k1) x U(k2), SU(k),
SO(2k), SO(2k+1), and Sp(2k) gauge groups and a variety of matter
representations, and compare to results in the literature for the original two
dimensional gauge theories. Finally, we perform consistency checks of
conjectures of Aharony et al that a two dimensional (2,2) supersymmetric pure
SU(k) gauge theory flows to a theory of k-1 free twisted chiral multiplets, and
also consider the analogous question in pure SO(3) theories. For one discrete
theta angle, the SO(3) theory behaves the same as the SU(2) theory; for the
other, supersymmetry is broken. We also perform consistency checks of analogous
statements in pure supersymmetric SO and Sp gauge theories in two dimensions.
