  We present a pedagogical overview of the nonperturbative mechanism that
endows gluons with a dynamical mass. This analysis is performed based on pure
Yang-Mills theories in the Landau gauge, within the theoretical framework that
emerges from the combination of the pinch technique with the background field
method. In particular, we concentrate on the Schwinger-Dyson equation satisfied
by the gluon propagator and examine the necessary conditions for obtaining
finite solutions within the infrared region. The role of seagull diagrams
receives particular attention, as do the identities that enforce the
cancellation of all potential quadratic divergences. We stress the necessity of
introducing nonperturbative massless poles in the fully dressed vertices of the
theory in order to trigger the Schwinger mechanism, and explain in detail the
instrumental role of these poles in maintaining the Becchi-Rouet-Stora-Tyutin
symmetry at every step of the mass-generating procedure. The dynamical equation
governing the evolution of the gluon mass is derived, and its solutions are
determined numerically following implementation of a set of simplifying
assumptions. The obtained mass function is positive definite, and exhibits a
power law running that is consistent with general arguments based on the
operator product expansion in the ultraviolet region. A possible connection
between confinement and the presence of an inflection point in the gluon
propagator is briefly discussed.
