2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/176518We review the description of the lowest-energy nucleon excitation -- the $Δ$(1232)-resonance. Much of the recent experimental effort has been focused on the precision measurements of the nucleon-to-$Δ$ 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-$Δ$ 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 $Δ$-resonance is described in detail. The two-photon exchange effects in the electroexcitation of the $\De$-resonance are addressed here as well.150 pp, 67 figs; final version - to appear in Physics ReportsHigh Energy Physics - PhenomenologyNuclear Theorytext