Spin glasses with multiple types

Spin glasses are models of statistical mechanics in which a large number of elementary units interact with each other in a disordered manner. In the simplest case, there are direct interactions between any two units in the system, and I will start by reviewing some of the key mathematical results in this context. For modelling purposes, it is also desirable to consider models with more structure, such as when the units are split into two groups, and the interactions only go from one group to the other one. I will then discuss some of the technical challenges that arise in this case, as well as recent progress.