We describe the background, design choices, and particular details of stress tests used as part of an overall supervisory regime, that is, their formal integration into the ongoing prudential supervision of banks and other large financial institutions. We then describe how the US Comprehensive Capital Analysis and Review (CCAR) and Dodd-Frank Act stress testing (DFAST) regime is designed and what that means for the macroprudential versus microprudential nature of US supervisory exercises. We argue that routine stress tests have the potential to substantially change the nature of the supervisory process. We also argue that a great deal depends on the philosophy underpinning modeling decisions, which has not received as much attention as scenario design, disclosure, or other stress test design choices.