Because of the strong electron correlation within the d-bands the majority of transition-metal oxides and halides are insulators and carry magnetic moments localized at the TM cations. Those two features are intimately interrelated and can be qualitatively rationalized within the Mott-Hubbard model framework. The configurations of the moments are governed by Hund's rules, favoring in general the high-spin HS state in which the Coulomb repulsion is the lowest. With the advent of diamond anvils cells (DAC) and the continued progress of high-pressure (sup 57)Fe Mossbauer spectroscopy (HP-MS) using select radioactive sources, studies to 200 GPa can now be achieved. We focus in the following subjects: methodology of HP-MS, particularly of (sup 57)Fe, using conventional point sources and miniature DACS; fundamentals of the Mott-Hubbard system; the metal-insulator transition and collapse of magnetism; and the breakdown of Hund's rules in the regime of very high-density of matter.