Mechanical deformability underpins many of the advantages of organic semiconductors. The mechanical properties of these materials are, however, diverse, and the molecular characteristics that permit charge transport can render the materials stiff and brittle. This review is a comprehensive description of the molecular and morphological parameters that govern the mechanical properties of organic semiconductors. Particular attention is paid to ways in which mechanical deformability and electronic performance can coexist. The review begins with a discussion of flexible and stretchable devices of all types, and in particular the unique characteristics of organic semiconductors. It then discusses the mechanical properties most relevant to deformable devices. In particular, it describes how low modulus, good adhesion, and absolute extensibility prior to fracture enable robust performance, along with mechanical "imperceptibility" if worn on the skin. A description of techniques of metrology precedes a discussion of the mechanical properties of three classes of organic semiconductors: A-conjugated polymers, small molecules, and composites. The discussion of each class of materials focuses on molecular structure and how this structure (and postdeposition processing) influences the solid-state packing structure and thus the mechanical properties. The review concludes with applications of organic semiconductor devices in which every component is intrinsically stretchable or highly flexible.