Metal halide perovskites represent a flourishing area of research, which is driven by both their potential application in photovoltaics and optoelectronics and by the fundamental science behind their unique optoelectronic properties. The emergence of new colloidal methods for the synthesis of halide perovskite nanocrystals, as well as the interesting characteristics of this new type of material, has attracted the attention of many researchers. This review aims to provide an up-to-date survey of this fast-moving field and will mainly focus on the different colloidal synthesis approaches that have been developed. We will examine the chemistry and the capability of different colloidal synthetic routes with regard to controlling the shape, size, and optical properties of the resulting nanocrystals. We will also provide an up-to-date overview of their postsynthesis transformations, and summarize the various solution processes that are aimed at fabricating halide perovskite-based nanocomposites. Furthermore, we will review the fundamental optical properties of halide perovskite nanocrystals by focusing on their linear optical properties, on the effects of quantum confinement, and on the current knowledge of their exciton binding energies. We will also discuss the emergence of nonlinear phenomena such as multiphoton absorption, biexcitons, and carrier multiplication. Finally, we will discuss open questions and possible future directions.