  In this review, we provide an up-to-date account of quantitative holographic
descriptions of the strongly coupled quark-gluon plasma (QGP) produced in
heavy-ion collisions, based on the class of gauge-gravity
Einstein-Maxwell-Dilaton (EMD) models. Holography is employed to tentatively
map the QCD phase diagram at finite temperature onto a dual theory of charged,
asymptotically AdS black holes in 5D. With a quantitative focus on the hot QCD
phase diagram, the EMD models reviewed are adjusted to describe lattice results
for the finite-temperature QCD equation of state, with 2+1 flavors and physical
quark masses, at zero chemical potential and vanishing electromagnetic fields.
The predictive power of EMD models is tested by quantitatively comparing their
predictions for the hot QCD equation of state at nonzero baryon density and the
corresponding state-of-the-art lattice QCD results. The shear and bulk
viscosities predicted by these EMD models are also compared to the
corresponding profiles favored by the latest phenomenological multistage models
describing different heavy-ion data. We report preliminary results from a
Bayesian analysis which provide systematic evidence that lattice results at
finite temperature and zero baryon density strongly constrains the free
parameters of EMD models. Remarkably, the set of parameters constrained by
lattice results at zero chemical potential produces EMD models in quantitative
agreement with lattice QCD results also at finite baryon density. We also
review results for equilibrium and transport properties from magnetic EMD
models, describing the QGP at finite temperatures and magnetic fields. Finally,
we provide a critical assessment of the main limitations and drawbacks of the
holographic models reviewed in the present work, and point out some
perspectives we believe are of fundamental importance for future developments.
