Early forming asteroids greater than ~50 km in diameter underwent extensive thermally driven differentiation, causing heating to a range of maximum temperatures. Some reached the stage of melting of initially incorporated water ice and experienced a range of temperature-dependent aqueous alteration processes; others underwent thermal metamorphism; yet others segregated metal cores; and some were heated to the point of extensive silicate melting, leading to volcanic intrusions or eruptions, controlled in part by the stresses induced in the crust by the prior internal evolution. We review advances in both the theoretical modeling of the migration of the various fluids involved in these processes and the experimental analyses of meteorites that provide constraints on the theoretical models. There is still uncertainty about many issues. Evidence from chondrite chemistry, petrography, and material properties is consistent with limited migration of aqueous fluids (essentially a closed system), although the oxygen isotope record has been used to support both open- and closed-system models, and remains a subject of debate. Opinions seem to be converging on the need for between 5% and 10% silicate melting to allow dense metallic melts to segregate to form cores. However, the locations of large bodies of silicate melt remain controversial, ideas being polarized between retention in asteroid mantles as magma oceans and rapid transfer to the base of the crust to pond as massive intrusions. Direct observations of (4) Vesta by the Dawn spacecraft have at least partially clarified our understanding of the chemical and tectonic states of differentiated asteroid crusts, but much remains to be understood about large-scale geodynamic processes.