  The nucleation of crystals in liquids is one of nature's most ubiquitous
phenomena, playing an important role in areas such as climate change and the
production of drugs. As the early stages of nucleation involve exceedingly
small time and length scales, atomistic computer simulations can provide unique
insight into the microscopic aspects of crystallization. In this review, we
take stock of the numerous molecular dynamics simulations that in the last few
decades have unraveled crucial aspects of crystal nucleation in liquids. We put
into context the theoretical framework of classical nucleation theory and the
state of the art computational methods, by reviewing simulations of e.g. ice
nucleation or crystallization of molecules in solutions. We shall see that
molecular dynamics simulations have provided key insight into diverse
nucleation scenarios, ranging from colloidal particles to natural gas hydrates,
and that in doing so the general applicability of classical nucleation theory
has been repeatedly called into question. We have attempted to identify the
most pressing open questions in the field. We believe that by improving (i.)
existing interatomic potentials; and (ii.) currently available enhanced
sampling methods, the community can move towards accurate investigations of
realistic systems of practical interest, thus bringing simulations a step
closer to experiments.

Materials Science