Cellular function often integrates biochemical and mechanical cues in what is known as mechanotransduction. Mechanotransduction is closely tied to cell shape during development, disease, and wound healing. In this talk, I will showcase how mathematical models have helped shed light on some fundamental problems in this area of research including how cell shape can alter biochemical signaling and how cell mechanics can alter cell shape. Throughout, I will highlight the challenges and opportunities for integrating mathematical models with experimental measurements.