Abstract: It has long been argued that the action of the Schwinger mechanism in the gauge sector of Quantum Chromodynamics leads to the generation of a gluon mass scale. Within this scenario, the analytic structure of the fundamental vertices is modified by the creation of scalar colored excitations with vanishing mass. In the limit of zero momentum transfer, these terms act as massless poles, providing the required conditions for the infrared stabilization of the gluon propagator, and producing a characteristic displacement to the associated Ward identities. In this article we offer an extensive overview of the salient notions and techniques underlying this dynamical picture. We place particular emphasis on recent developments related to the exact renormalization of the mass, the nonlinear nature of the pole equation, and the key role played by the Fredholm alternative theorem.