  In this contribution I present a few selected topics of recent theoretical
developments of relevance for the NICA facility under construction. In a first
part, I discuss new aspects of the QCD phase diagram like the possible
existence of a critical endpoint of first-order phase transitions from the
perspective of generalizations of the 3-flavor PNJL model including the
conjecture of a universal pressure for the onset of deconfinement in heavy-ion
collisions and astrophysics. A second part is devoted to first results of the
newly constructed event simulator (THESEUS) which is based on the
particlization of the former three-fluid hydrodynamics code by Ivanov, Russkikh
and Toneev that allows also to study the role of hadronic final state
interactions. Possible signals of the mixed phase accessible at NICA are
considered. In particular, the robustness of the baryon-stopping signal of
deconfinement and the occurrence of antiflow for protons have been investigated
for Au+Au collisions in the range of the NICA-MPD energy scan for $\sqrt{s}
\sim 6 \dots 8$ GeV. This signal is reflected also in the flow pattern of light
nuclear clusters, in particular deuterons. The sharp peak for the $K^+/\pi^+$
ratio at $\sqrt{s} \sim 8$ GeV (the "horn" effect) is not obtained in the
present version of THESEUS and calls for improvement of the equation of state
input. I report the recent progress in developing a generalized Beth-Uhlenbeck
approach to a unified description of quark-hadron matter which includes now
strangeness and reveals a new mechanism for explaining the $K^+/\pi^+$ ratio
due to the pronounced occurrence of an anomalous mode in the $K^+$ at finite
baryochemical potentials.
