Perovskite solar cells (PSCs) have been intensively investigated over the last several years. Unprecedented progress has been made in improving their power conversion efficiency; however, the stability of perovskite materials and devices remains a major obstacle for the future commercialization of PSCs. In this review, recent progress in PSCs is summarized in terms of the hybridization of compositions and device architectures for PSCs, with special attention paid to device stability. A brief history of the development of PSCs is given, and their chemical structures, optoelectronic properties, and the different types of device architectures are discussed. Then, perovskite composition engineering is reviewed in detail, with particular emphasis on the cationic components and their impact on film morphology, the optoelectronic properties, device performance, and stability. In addition, the impact of two-dimensional and/or one-dimensional and nanostructured perovskites on structural and device stability is surveyed. Finally, a future outlook is proposed for potential resolutions to overcome the current issues.