  We review the current status of nonperturbative studies of gauge field theory
using the Dyson-Schwinger equation formalism and its application to hadronic
physics. We begin with an introduction to the formalism and a discussion of
renormalisation in this approach. We then review the current status of studies
of Abelian gauge theories [e.g., strong coupling quantum electrodynamics]
before turning our attention to the non-Abelian gauge theory of the strong
interaction, quantum chromodynamics. We discuss confinement, dynamical chiral
symmetry breaking and the application and contribution of these techniques to
our understanding of the strong interactions.
