  The past 20 years have witnessed a renewal of interest in the subject of
double-diffusive processes in astrophysics, and their impact on stellar
evolution. This lecture aims to summarize the state of the field as of early
2019, although the reader should bear in mind that it is rapidly evolving. An
Annual Review of Fluid Mechanics article entitled "Double-diffusive convection
at low Prandtl number" (Garaud, 2018) contains a reasonably comprehensive
review of the topic, up to the summer of 2017. I focus here on presenting what
I hope are clear derivations of some of the most important results with an
astrophysical audience in mind, and discuss their implications for stellar
evolution, both in an observational context, and in relation to previous work
on the subject.
