This dissertation explores the effects of pressure on the magnetic remanence of iron-nickel and iron-silicon alloys relevant to the solid inner cores of the terrestrial planets and Earth’s moon. The Earth’s inner core likely comprises mostly pure iron in a hexagonal close packed (hcp) structure. Experiments on pure iron powder and foil were carried out up to 21 GPa at room temperature. The most important conclusion from this work is that either hcp-iron is ferromagnetic or that a poorly understood, intermediate hcp phase of iron is ferromagnetic. It was also determined that the results must be corrected for magnetic shape anisotropy, which is related either to the original sample material (foil) or how the bulk sample volume changes shape due to increasing oblateness of the chamber during pressurization. Fe-Ni alloys in the face centered cubic (fcc) phase with compositions around Fe64Ni36, called Invar, exhibit near-null thermal expansion, making them useful for technological applications. Models explaining the Invar effect evoke magnetovolume effect that compensate for thermal expansion. Previous work suggested that the Curie temperature of Fe64Ni36 decreases 35 K per GPa, which predicts that around 5 GPa, Fe64Ni36 will turn paramagnetic. Our experiments on Fe64Ni36 found a marked decrease in magnetization between 5-7 GPa, consistent with former studies, but that it remains ferromagnetic until 16 GPa. The magnetic remanence of low Ni Invar alloys increases faster with pressure than for other body-centered-cubic compositions due to the higher magnetostriction of the low Ni Invar metals. Experimental results on body centered cubic (bcc) Fe-Ni alloys match well with those for pure iron-- again leading to the conclusion that either an intermediate hcp phase, or that the hcp phase itself, is ferromagnetic. The ubiquitous enhancement in magnetization under pressure, or during pressure release, of the Fe-Ni and Fe-Si alloys is associated with strain-induced martensitic effects. Finally, a defocused laser heating technique was developed to measure the Curie temperature in diamond or moissanite anvil cells. Preliminary results on titanomagnetite (Fe2.4Ti0.6O4) are broadly consistent with previous work.