  In this short review, we outline three sets of developments in understanding
heterotic string compactifications. First, we outline recent progress in
heterotic analogues of quantum cohomology computations. Second, we discuss a
potential swampland issue in heterotic strings, and new heterotic string
constructions that can be used to fill in the naively missing theories. Third,
we discuss recent developments in string compactifications on stacks and their
applications, concluding with an outline of work-in-progress on heterotic
string compactifications on gerbes.
