This talk will focus on how methods from homotopy theory can be used to tackle questions regarding diffeomorphisms of disks. I'll first try to convince the audience that we ought to care about diffeomorphisms of disks and then describe some different ways to think about related questions.There will be a short and non-technical description of Algebraic K-theory, culminating in a landmark result of  Farrell–Hsiang that relates the homotopy type of Diff(D^n) to the K-theory of the integers in a stable range.