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This article is devoted to an overview of superstring perturbation theoryfrom the point of view of super Riemann surfaces. We aim to elucidate some ofthe subtleties of superstring perturbation that caused difficulty in the earlyliterature, focusing on a concrete example -- the $SO(32)$ heterotic stringcompactified on a Calabi-Yau manifold, with the spin connection embedded in thegauge group. This model is known to be a significant test case for superstringperturbation theory. Supersymmetry is spontaneously broken at 1-loop order, andto treat correctly the supersymmetry-breaking effects that arise at 1- and2-loop order requires a precise formulation of the procedure for integrationover supermoduli space. In this paper, we aim as much as possible for aninformal explanation, though at some points we provide more detailedexplanations that can be omitted on first reading.

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