  The goal of these lecture notes is to survey progress on the global Langlands
reciprocity conjecture for $\mathrm{GL}_n$ over number fields from the last
decade and a half. We highlight results and conjectures on Shimura varieties
and more general locally symmetric spaces, with a view towards the
Calegari-Geraghty method to prove modularity lifting theorems beyond the
classical setting of Taylor-Wiles.
