This talk will begin with a non-technical introduction to the local Langlands correspondence. This correspondence famously relates arithmetic data with representation-theoretic data. The two main examples in this talk will be GL(n) and SL(n). For GL(n) there is a perfect correspondence, for SL(n) the correspondence is a little more subtle, with L-packets making an appearance: an L-packet comprises finitely many irreducible representations. I will describe the parametrisation of these L-packets, and will illustrate with the example of SL(2).