Over the last few years, string compactifications have come back into fashion as an approach to phenomenology (KKLT, landscapes, ...), and nonperturbative corrections to superpotentials play an important role. Most of the work done recently revolves around type II string compactifications with fluxes, but a smaller community has also been interested in using heterotic strings to the same ends. However, nonperturbative corrections to heterotic spacetime superpotentials have historically been more difficult to compute. In this talk, we will describe some work on computing stringy nonperturbative corrections to heterotic spacetime superpotentials. Technically, this amounts to understanding (0,2) generalizations of the A and B model topological field theories, meaning (0,2) generalizations of curve-counting, which also has applications to understanding (0,2) mirror symmetry.