The theory of unitary representations originated in the past century as a natural evolution of classical Fourier analysis. In spite of the extremely significant contributions made by Langlands, Harish-Chandra and many other mathematicians, the problem of finding \emph{all} the unitary irreducible representations of a real reductive group remains a challenge: to this day, a complete answer is only known for a handful of groups. In this talk, I will describe some recent progress in the field.