Hybrid perovskites are currently one of the most active fields of research owing to their enormous potential for photovoltaics. The performance of 3D hybrid organic-inorganic perovskite solar cells has increased at an incredible rate, reaching power conversion efficiencies comparable to those of many established technologies. However, the commercial application of 3D hybrid perovskites is inhibited by their poor stability. Relative to 3D hybrid perovskites, low-dimensional - that is, 2D - hybrid perovskites have demonstrated higher moisture stability, offering new approaches to stabilizing perovskite-based photovoltaic devices. Furthermore, 2D hybrid perovskites have versatile structures, enabling the fine-tuning of their optoelectronic properties through compositional engineering. In this Review, we discuss the state of the art in 2D perovskites, providing an overview of structural and materials engineering aspects and optical and photophysical properties. Moreover, we discuss recent developments along with the main limitations of 3D perovskites and assess the advantages of 2D perovskites over their 3D parent structures in terms of stability. Finally, we review recent achievements in combining 3D and 2D perovskites as an approach to simultaneously boost device efficiency and stability, paving the way for mixed-dimensional perovskite solar cells for commercial applications.