Recent planetary space missions, new experimental data, and advanced numerical techniques have helped to improve our understanding of the deep interiors of the terrestrial planets and moons. In the present review, we summarize recent insights into the state and composition of their iron (Fe)-rich cores, as well as recent findings about the magnetic field evolution of Mercury, the Moon, Mars, and Ganymede. Crystallizing processes in iron-rich cores that differ from the classical Earth case (i.e., Fe snow and iron sulfide (FeS) crystallization) have been identified and found to be important in the cores of terrestrial bodies. The Fe snow regime occurs at pressures lower than that in the Earth’s core on the iron-rich side of the eutectic, where iron freezes first close to the core–mantle boundary rather than in the center. FeS crystallization, instead, occurs on the sulfur-rich side of the eutectic. Depending on the core temperature profile and the pressure range considered, FeS crystallizes either in the core center or close to the core–mantle boundary. The consequences of the various crystallizing mechanisms for core dynamics and magnetic field generation are discussed. For the Moon, revised paleomagnetic data obtained with advanced techniques suggest a peculiar history of its internal dynamo, with an early strong field persisting between 4.25 and 3.5 Ga, and subsequently a much weaker field. In addition, the long-lasting dynamo and the possible presence of an inner core, as inferred from a revised interpretation of Apollo seismic data, suggest core crystallization as a viable process of magnetic field generation for a substantial period during lunar evolution. The present-day magnetic fields of Mercury and Ganymede (if they occur on the iron-rich side of the Fe–FeS eutectic) and the related dynamo action are likely generated in the Fe snow regime and seem to be recent features. An earlier dynamo in Mercury would have been powered differently. For Mercury, MESSENGER data further suggest core formation under reducing conditions that may have resulted in an Fe–S–Si composition, further complicating the core crystallization process. Mars, with its early and strong paleo-field, likely has not yet started to freeze out an inner iron core.