Achieving technologically relevant performance and stability for optoelectronics, energy conversion, photonics, spintronics and quantum devices requires creating atomically precise materials with tailored homo- and hetero-interfaces, which can form functional hierarchical assemblies. Nature employs tunable sequence chemistry to create complex architectures, which efficiently transform matter and energy, however, in contrast, the design of synthetic materials and their integration remains a long-standing challenge. Organic-inorganic two-dimensional halide perovskites (2DPKs) are organic and inorganic two-dimensional layers, which self-assemble in solution to form highly ordered periodic stacks. They exhibit a large compositional and structural phase space, which has led to novel and exciting physical properties. In this Review, we discuss the current understanding in the structure and physical properties of 2DPKs from the monolayers to assemblies, and present a comprehensive comparison with conventional semiconductors, thereby providing a broad understanding of low-dimensional semiconductors that feature complex organic-inorganic hetero-interfaces. This Review provides an overview of the current understanding of the physics of organic-inorganic two-dimensional halide perovskites.