  A large class of (0,2) Calabi-Yau $\sigma$-models and Landau-Ginzburg
orbifolds are shown to arise as different ``phases'' of supersymmetric gauge
theories. We find a phenomenon in the Landau-Ginzburg phase which may enable
one to understand which Calabi-Yau $\sigma$-models evade destabilization by
worldsheet instantons. Examples of (0,2) Landau-Ginzburg vacua are analyzed in
detail, and several novel features of (0,2) models are discussed. In
particular, we find that (0,2) models can have different quantum symmetries
from the (2,2) models built on the same Calabi-Yau manifold, and that a new
kind of topology change can occur in (0,2) models of string theory.
