Category theory allows a precise formulation of relationships between structures that emerge from seemingly different contexts across mathematics. One would like to study not just the properties of one particular group, for example, but of the category of groups and group homomorphisms between them as a whole. Category theorists would then like to do the same with their own subject, and study not just some particular category but rather the whole picture of categories, functors, and natural transformations. This is a preliminary example of a 2-category. This talk will be about 2-categories and some of their generalisations.