  Mirror symmetry of the type II string has a beautiful generalization to the
heterotic string. This generalization, known as (0,2) mirror symmetry, is a
field still largely in its infancy. We describe recent developments including
the ideas behind quantum sheaf cohomology, the mirror map for deformations of
(2,2) mirrors, the construction of mirror pairs from worldsheet duality, as
well as an overview of some of the many open questions. The (0,2) mirrors of
Hirzebruch surfaces are presented as a new example.

High Energy Physics - Theory;Algebraic Geometry