Stimuli-responsive materials undergo triggered changes when presented with specific environmental cues. These dynamic systems can leverage biological signals found locally within the body as well as exogenous cues administered with spatiotemporal control, providing powerful opportunities in next-generation diagnostics and personalized medicine. Here, we review the synthetic and strategic advances used to impart diverse responsiveness to a wide variety of biomaterials. Categorizing systems on the basis of material type, number of inputs, and response mechanism, we examine past and ongoing efforts toward endowing biomaterials with customizable sensitivity. We draw an analogy to computer science, whereby a stimuli-responsive biomaterial transduces a set of inputs into a functional output as governed by a user-specified logical operator. We discuss Boolean and non-Boolean operations, as well as the various chemical and physical modes of signal transduction. Finally, we examine current limitations and promising directions in the ongoing development of programmable stimuli-responsive biomaterials.