Metastable liquids

How far can one supercool a liquid before it crystallizes? How much can one stretch it before cavitation occurs ? In order to answer such questions, we have studied liquid helium, a model system. In this review, we show the limitations of the elementary 'standard nucleation theory'. We then show that the existence of 'spinodal' limits needs to be considered in the framework of 'density functional' methods. We also briefly consider the possibility of nucleation by quantum tunnelling. The main emphasis is on cavitation and crystallization in liquid helium, but we also mention several connections with more classical systems, in particular water.