I will talk about three approaches to deepen our understanding of the high-baryon state of matter: The first one is the pQCD analysis with the effect of resummation. It is said that the pQCD EoS is uncertain unless the baryon density is unphysically large, but this is caused by an improper choice of small scale. A simple resummation can change the situation drastically to narrow the uncertainty band. The second one is the interacting hadronic model that complements the pQCD analysis, but an excluded volume effect with hard core would easily violate the causality. I will discuss that the Carnahan-Starling implementation of the smeared interacting core works well with phenomenology. Finally, I will introduce a bit of academic thinking about nuclear matter under strong magnetic fields described by the Skyrme model, which is however rather model independent in a sense that the important physics is brought in by the anomalous coupling between the density and the magnetic field.