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Let $G$ be a reductive group over a nonarchimedean local field $F$. In thequest for a classification of irreducible smooth representations of $G$, it iscritical to understand the case of supercuspidal representations -- those whosematrix coefficients are compactly supported modulo the center. Progress inunderstanding these representations has been continuous over the past fiftyyears. In "tame" cases where the residual characteristic of $F$ is big enoughfor $G$, J.-K. Yu described in 2001 a general construction of supercuspidalrepresentations, building on a large body of work. But recent developments havemade the general picture much more complete and much clearer. For instance, thework of J. Fintzen, T. Kaletha and L. Spice provides (in the tame case) aclassification of supercuspidal representations, an explicit formula for"almost all" their characters, and an explicit construction of a localLanglands correspondence for supercuspidal $L$-packets. While the basicconstructions involve Bruhat--Tits buildings and representations of finitegroups, the resulting character formulas and the description of $L$-packetshave striking parallels with the case of real groups

Progr\`es r\'ecents sur les repr\'esentations supercuspidales