  We review the description of the lowest-energy nucleon excitation -- the
$\Delta$(1232)-resonance. Much of the recent experimental effort has been
focused on the precision measurements of the nucleon-to-$\Delta$ transition by
means of electromagnetic probes. We confront the results of these measuremnts
with the state-of-the-art calculations based on chiral effective-field theories
(EFT), lattice QCD, large-$N_c$ relations, perturbative QCD, and QCD-inspired
models. We also discuss the link of the nucleon-to-$\Delta$ form factors to
generalized parton distributions (GPDs). Some of the theoretical approaches are
reviewed in detail, in particular, recent dynamical and unitary-isobar models
of pion electroproduction, which are extensively used in the interpretation of
experiments. Also, the novel extension of chiral EFTs to the energy domain of
the $\Delta$-resonance is described in detail. The two-photon exchange effects
in the electroexcitation of the $\De$-resonance are addressed here as well.
