The local Langlands correspondence conjectures a finite-to-one map from the isomorphism classes of smooth irreducible representations of a p-adic group to conjugacy classes of certain morphisms called L-parameters. These L-parameters are in general difficult to describe, and classifying the representations in the corresponding "L-packet" can be quite tricky. However, in the case of a particularly nice class of representations called toral supercuspidal representations, Kaletha has shown that it is possible to write down the local Langlands correspondence quite explicitly. The goal of this talk is to state Kaletha's classification of toral supercuspidal L-parameters and parametrization of their corresponding L-packets, and (time permitting) compute an example for a small group. I will begin by discussing the (refined) local Langlands conjecture in general, then briefly review the theory of supercuspidal representations (including Yu's construction) before focusing on the toral supercuspidal setting. The main reference for this talk is Kaletha's 2017 paper "Regular Supercuspidal representations."