Flexible and stretchable solar cells have attracted much attention in both the academic and industrial communities due to their huge application potential in many areas, such as buildings, decoration, transportation, fashion, and portable and wearable electronics. In recent years, perovskite solar cells (PSCs) have emerged as the most promising photovoltaic technology, simultaneously offering high efficiency, light weight, low cost, low‐temperature and solution‐processing ability, and material flexibility, which are essential for flexible and stretchable applications. Here, a detailed review is presented on the development of flexible and stretchable PSCs, in terms of the choices of active, interfacial, conductive, and substrate materials, as well as device structures. First, some fundamental principles of PSCs regarding their suitability for flexible and stretchable applications are introduced. Then, the developments and evolving methods of several important materials of flexible devices, including flexible and stretchable substrates, electrodes, and interfacial layers, are summarized. The design of the device structure, which is directly related to the performance in flexibility and stretchability, is also discussed. Finally, conclusions are presented and some promising research directions for flexible and stretchable PSCs in the future are highlighted.