  We review the covariant density functional approach to the equation of state
of the dense nuclear matter in compact stars. The main emphasis is on the
hyperonization of the dense matter, and the role played by the
$\Delta$-resonances. The implications of hyperonization for the astrophysics of
compact stars, including the equation of state, composition, and stellar
parameters are examined. The mass-radius relation and tidal deformabilities of
static and rapidly rotating (Keplerian) configurations are discussed in some
detail. We briefly touch upon some other recent developments involving
hyperonization in hot hypernuclear matter at high- and low-densities.
