Electronic/magnetic transitions and their structural consequences in Fe-based Mott insulators in a regime of very high static density are the main issue of this short review paper. The paper focuses on the above-mentioned topics based primarily on our previous and ongoing experimental HP studies employing: (i) diamond anvil cells, (ii) synchrotron X-ray diffraction, (iii) 57Fe Mössbauer spectroscopy, (iv) electrical resistance and (v) X-ray absorption spectroscopy. It is shown that applying pressure to such strongly correlated systems leads to a number of changes; including quenching of the orbital moment, quenching of Jahn-Teller distortion, spin crossover, inter-valence charge transfer, insulator–metal transition, moment collapse and volume collapse. These changes may occur simultaneously or sequentially over a range of pressures. Any of these may be accompanied by or be a consequence of a structural phase transition; namely, a change in crystal symmetry. Analyzing this rich variety of phenomena we show the main scenarios which such strongly correlated systems may undergo on the way to a correlation breakdown (Mott transition). To illustrate these scenarios we present recent results for MFeO3 (M = Fe, Ga, Lu, Eu, Pr) and CaFe2O4 ferric oxides; FeCl2 and FeI2 ferrous halides, and FeCr2S4 sulfide. Fe3O4 is given as an example case for the impact of Mössbauer Spectroscopy on High Pressure Crystallography studies.