  Properties of high-density strong-interaction matter of relevance for
astrophysical scenarios that involve neutron stars are discussed. It is argued
that theoretical and experimental insights from the small baryo-chemical
potential ($\mu_B$) and high-temperature regions of the QCD phase diagram can
guide realistic model building at high density, as this regime is currently not
accessible to first-principles numerical calculations of the QCD partition
function. Special attention is payed to the chiral properties of high-density
matter and the nature of a possible first-order chiral phase transition. In
this transition hadronic parity-partners, in particular baryons, become
spectrally degenerate with finite (pole) masses, as expected from general
insight into the mass generation in QCD. Possible signals in heavy-ion
dielectron production at beam energies of a few GeV are discussed. Based on
evidence for an emergent "chiral spin symmetry" above the pseudo-critical
chiral transition temperature at small $\mu_B$, speculations on the physical
state of dense hadronic matter beyond the chiral phase transition are
presented.
