We demonstrate the assembly of biohybrid materials from engineered tissues and synthetic polymer thin films. The constructs were built by culturing neonatal rat ventricular cardiomyocytes on polydimethylsiloxane thin films micropatterned with extracellular matrix proteins to promote spatially ordered, two-dimensional myogenesis. The constructs, termed muscular thin films, adopted functional, three-dimensional conformations when released from a thermally sensitive polymer substrate and were designed to perform biomimetic tasks by varying tissue architecture, thin-film shape, and electrical-pacing protocol. These centimeter-scale constructs perform functions as diverse as gripping, pumping, walking, and swimming with fine spatial and temporal control and generating specific forces as high as 4 millinewtons per square millimeter.