Schwinger-Dyson equations (SDEs) provide a natural staring point to study
non-perturbative phenomena such as dynamical chiral symmetry breaking in gauge
field theories. We briefly review this research in the context of quenched
quantum electrodynamics (QED) and discuss the advances made in the gradual
improvement of the assumptions employed to solve these equations. We argue that
these attempts render the corresponding studies more and more reliable and
suitable for their future use in the more realistic cases of unquenched QED,
quantum chromodynamics (QCD) and models alternative to the standard model of
particle physics.Comment: 8 pages, 1 figure, Talk given at the X Mexican School of Particles
and Fields, Playa del Carmen, Mexico, 2002 (uses AIP style files
