Electromagnetic excitation of the ∆(1232)-resonance

We review the description of the lowest-energy nucleon excitation — the ∆(1232)-resonance. Much of the recent experimental effort has been focused on the precision measurements of the nucleon-to-∆ 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-Nc relations, perturbative QCD, and QCD-inspired models. We also discuss the link of the nucleon-to-∆ 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 ∆-resonance is described in detail. The two-photon exchange effects in the electroexcitation of the ∆-resonance are addressed here as well.