During the last half century, a large proportion of number theorists have been occupied with the Langlands program, which proposes the existence of certain correspondences between automorphic and Galois representations, going vastly beyond quadratic reciprocity or class field theory. We will discuss the origins of the Langlands program and try to explain how methods from higher category theory, representation theory, and also $p$-adic geometry have played a role in transforming the field during the last two decades. If time permits, we will conclude by describing some of our own contributions and possible future directions.