Hadron physics stands somewhere in the diffuse intersection between nuclear and particle physics and relies largely on the use of models. Historically, around 1930, the first nuclear physics models known as the liquid drop model and the semi-empirical mass formula established the grounds for the study of nuclei properties and nuclear structure. These two models are parameter dependent. Nowadays, around 500 hundred non-relativistic (Skyrme-type) and relativistic models are available in the literature and largely used and the vast majority are parameter dependent models. In this review I discuss some of the shortcomings of using non-relativistic models and the advantages of using relativistic ones when applying them to describe hadronic matter. I also show possible applications of relativistic models to physical situations that cover part of the QCD phase diagram: I mention how the description of compact objects can be done, how heavy-ion collisions can be investigated and particle fractions obtained and show the relation between liquid-gas phase transitions and the pasta phase.
