Dynamical resonances were introduced in the 1970s by Ruelle, Pollicott, Bowen, and others to understand the decay of correlations in hyperbolic flows, a key aspect of long-term dynamical behavior. In this talk will review the concept of dynamical resonances, particularly its modern approach using microlocal analysis. Later in this presentation, I will report how these techniques have very recently been applied to develop a higher rank spectral theory for Anosov representations, which over the past decades have intensively been studied in the context of higher Teichmüller theory.