The local Langlands correspondence (LLC) is a kaleidoscope of conjectures relating local Galois theory, complex Lie theory, and representations of $p$-adic groups. This talk will give an introduction to the part of the LLC involving unipotent representations. Reducing modulo $p$, we can move from representations of $p$-adic groups to representations of finite reductive groups, which have a rich structure developed by Deligne–Lusztig. I will talk about joint work with Anne-Marie Aubert and Dan Ciubotaru in which we lift some of this structure to $p$-adic groups. I will not assume previous familiarity with these topics; instead I’ll give an introduction to these ideas via examples.