  The task of mapping and explaining the spectrum of baryons and the structure
of these states in terms of quarks and gluons is a longstanding challenge in
hadron physics, which is likely to persist for another decade or more. We
review the progress made in this topic using a functional method based on
Dyson-Schwinger equations. This framework provides a non-perturbative,
Poincar\'e-covariant continuum formulation of Quantum Chromodynamics which is
able to extract novel insight on baryon properties since the physics at the
hadron level is directly related with the underlying quark-gluon substructure,
via convolution of Green functions.
