From correlation functions to glueballs

he spectrum of quantum chromodynamics consists of different types of hadrons, the most prominent ones being mesons and baryons, which consist of two and three (anti-)quarks, respectively. In addition, there are other possibilities which are collectively called exotic hadrons. These include states consisting only of gluons, so-called glueballs. The determination of their properties is an active field of research both experimentally and theoretically. In this talk, I will introduce functional bound state equations as a theoretical tool to investigate such states and to understand the mechanisms behind their formation. Their applications range from model-driven investigations to first-principles calculations. As an example of the latter, I will present results for the spectrum of glueballs in pure gauge theory.