In this article, we provide a control-theoretic perspective on the research area of behavior trees in robotics. The key idea underlying behavior trees is to make use of modularity, hierarchies, and feedback in order to handle the complexity of a versatile robot control system. Modularity is a well-known tool to handle software complexity by enabling the development, debugging, and extension of separate modules without detailed knowledge of the entire system. A hierarchy of such modules is natural, since robot tasks can often be decomposed into a hierarchy of subtasks. Finally, feedback control is a fundamental tool for handling uncertainties and disturbances in any low-level control system, but in order to enable feedback control on the higher level, where one module decides what submodule to execute, information regarding the progress and applicability of each submodule needs to be shared in the module interfaces. We describe how these three concepts can be used in theoretical analysis, practical design, and extensions and combinations with other ideas from control theory and robotics.