  We review the spectrum and electromagnetic properties of baryons described as
relativistic three-quark bound states within QCD. The composite nature of
baryons results in a rich excitation spectrum, whilst leading to highly
non-trivial structural properties explored by the coupling to external
(electromagnetic and other) currents. Both present many unsolved problems
despite decades of experimental and theoretical research. We discuss the
progress in these fields from a theoretical perspective, focusing on
nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger
and Bethe-Salpeter equations. We give a systematic overview as to how results
are obtained in this framework and explain technical connections to lattice
QCD. We also discuss the mutual relations to the quark model, which still
serves as a reference to distinguish 'expected' from 'unexpected' physics. We
confront recent results on the spectrum of non-strange and strange baryons,
their form factors and the issues of two-photon processes and Compton
scattering determined in the Dyson-Schwinger framework with those of lattice
QCD and the available experimental data. The general aim is to identify the
underlying physical mechanisms behind the plethora of observable phenomena in
terms of the underlying quark and gluon degrees of freedom.
