  Let $G$ be a reductive group over a nonarchimedean local field $F$. In the
quest for a classification of irreducible smooth representations of $G$, it is
critical to understand the case of supercuspidal representations -- those whose
matrix coefficients are compactly supported modulo the center. Progress in
understanding these representations has been continuous over the past fifty
years. In "tame" cases where the residual characteristic of $F$ is big enough
for $G$, J.-K. Yu described in 2001 a general construction of supercuspidal
representations, building on a large body of work. But recent developments have
made the general picture much more complete and much clearer. For instance, the
work of J. Fintzen, T. Kaletha and L. Spice provides (in the tame case) a
classification of supercuspidal representations, an explicit formula for
"almost all" their characters, and an explicit construction of a local
Langlands correspondence for supercuspidal $L$-packets. While the basic
constructions involve Bruhat--Tits buildings and representations of finite
groups, the resulting character formulas and the description of $L$-packets
have striking parallels with the case of real groups
