  We review the physics of hyperons and $\Delta$-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
$\beta$-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 $\Delta$-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
$\Delta$-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.
