Economists have extensively analyzed the regulation of banks and the banking industry, but have devoted considerably less attention to bank supervision as a distinct activity. Indeed, much of the banking literature has used the terms "supervision" and "regulation" interchangeably. This paper provides a heuristic review of the economics literature on microprudential bank supervision, highlighting broad findings and existing gaps, especially those related to work on supervision's theoretical underpinnings. The theoretical literature examining the motivation for supervision (monitoring and oversight) as an activity distinct from regulation (rulemaking) is just now emerging and has considerable room to grow. Meanwhile, the empirical literature assessing the impact of supervision is more substantial. Initial results suggest that supervision reduces risk at banks without meaningfully reducing profitability. The evidence is more mixed about whether more intensive supervision reduces credit supply. The channels through which supervision achieves these results have yet to be fully explored, however. Finally, there is a body of work exploring how supervisory incentives - at both the individual and institutional levels-affect outcomes. Supervisory incentives are fundamentally entwined with the theoretical rationale for supervision as a distinct activity and with empirical assessments of its impact. Drawing these links more clearly is an additional area for fruitful future work.