Is there any structure to the set of algebraic extensions of the field of rational numbers ℚ? Can we describe the linear representations of its absolute Galois group? These questions lead to class field theory and, ultimately, the Langlands program. They become far simpler if ℚ is replaced by a local field such as ℚ_p. We will give a motivated introduction to the “local Langlands program”, which is an attempt to describe all the representations of the absolute Galois group via objects that seem to have nothing to do with Galois theory.