A major goal of the Langlands program is to describe the multiplicity of an irreducible discrete automorphic representation of a connected reductive group G in its discrete L2-spectrum. The first goal of this talk is to explain work from the last few years which gives the first conjectural formula for this multiplicity for general G over a global field, as envisioned by Kottwitz in 1984. We then discuss recent work which we hope lays the foundations for proving cases of these formulas using the geometric framework of Fargues and Scholze.