This talk will explore one of my favorite themes in mathematics: the abstract notion of a trace and its manifestation via fixed points in geometry and partition functions in quantum mechanics. This relation, which I explored in a series of papers with David Nadler, gives rise to a sequence of increasingly sophisticated character formulas, as well as a broader sense of what characters are. I will conclude with a perspective on L-functions of Galois representations as characters, developed in my joint work with Yiannis Sakellaridis and Akshay Venkatesh.