  Metal halide perovskites represent a flourishing area of research, driven by
both their potential application in photo-voltaics and optoelectronics, and for
the fundamental science underpinning their unique optoelectronic properties.
The advent of colloidal methods for the synthesis of halide perovskite
nanocrystals has brought to the attention inter-esting aspects of this new type
of materials, above all their defect-tolerance. This review aims to provide an
updated survey of this fast-moving field, with a main focus on their colloidal
synthesis. We examine the chemistry and the ca-pability of different colloidal
synthetic routes to control the shape, size and optical properties of the
resulting nano-crystals. We also provide an up to date overview of their
post-synthesis transformations, and summarize the various so-lution processes
aimed at fabricating halide perovskite-based nanocomposites. We then review the
fundamental optical properties of halide perovskite nanocrystals, by focusing
on their linear optical properties, on the effects of quantum confinement and,
then, on the current knowledge of their exciton binding energies. We also
discuss the emergence of non-linear phenomena such as multiphoton absorption,
biexcitons and carrier multiplication. At last, we provide an outlook in the
field, with the most cogent open questions and possible future directions.
