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We review the physics of hyperons and $Δ$-resonances in dense matter in compact stars. The covariant density functional approach to the equation of state and composition of dense nuclear matter in the mean-field Hartree and Hartree-Fock approximation is presented, with regimes covering cold $β$-equilibrated matter, hot and dense matter with and without neutrinos relevant for the description of supernovas and binary neutron star mergers, as well as dilute expanding nuclear matter in collision experiments. We discuss the static properties of compact stars with hyperons and $Δ$-resonances in light of constraints placed in recent years by the multimessenger astrophysics of compact stars on the compact stars' masses, radii, and tidal deformabilities. The effects of kaon condensation and strong magnetic fields on the composition of hypernuclear stars are also discussed. The properties of rapidly rotating compact hypernuclear stars are discussed and confronted with the observations of 2.5-2.8 solar mass compact objects in gravitational wave events. We further discuss the cooling of hypernuclear stars, the neutrino emission reactions, hyperonic pairing, and the mass hierarchy in the cooling curves that arises due to the onset of hyperons. The effects of hyperons and $Δ$-resonances on the equation of state of hot nuclear matter in the dense regime, relevant for the transient astrophysical event and in the dilute regime relevant to the collider physics is discussed. The review closes with a discussion of universal relations among the integral parameters of hot and cold hypernuclear stars and their implications for the analysis of binary neutron star merger events.