Precision medicine requires materials and devices that can sense and adapt to dynamic physiological and pathological conditions. This motivates the design and manufacture of biohybrid materials that mimic the responsive behaviors demonstrated by natural biological systems. Two parallel approaches to biohybrid design are presented—biomimetics and biointegration. Biohybrid hydrogels that mimic the form and function of natural materials, or that integrate living cells or bioactive moieties, can respond to a range of environmental stimuli in parallel, including heat, light, pH, hydration, enzymes, and electric, mechanical, and magnetic forces. A range of examples that illustrate the tremendous potential of this nascent discipline are presented, and ongoing technical challenges related to manufacturing, storage, transport, and external noninvasive control of these materials that will need to be overcome in the coming years are outlined. The ethical, educational, and regulatory challenges that will govern translation of biohybrid design into medical applications are also discussed. Personalized medical therapies that target the precise needs of patients are a critically needed and expanding market. Biohybrid design offers the unique ability to manufacture materials and devices that match the dynamic and patient‐specific in vivo environment, promising to generate more effective and safe therapies that enable personalized care.