The Earth is a heat engine, where large differences in temperature between the interior and the surface drive large-scale movement that manifests as plate tectonics and the geomagnetic field that protects us from the Sun’s harmful charged particles. Decay of the long-lived radioactive elements U, Th, and K is expected to contribute as much as 45% of the current heat production in the Earth, and that heat production was five times higher early in Earth’s history. It is unclear how this heat source affects the thermal and dynamic evolution of the Earth’s core and mantle and how that contribution has changed over geologic time. This dissertation addresses this problem in several different ways. This work represents the first high-pressure, high-temperature metal–silicate partitioning experiments for U, Th, and K in the laser-heated diamond anvil cell at conditions relevant to core formation. A chemical model is developed using parameterization of these partitioning data to constrain the concentrations of each of these elements in the core. Using a numerical calculation, it is then determined how that radioactive heat would contribute to the core’s energy and entropy budget through time. One finds that, despite its strong lithophile nature at the surface, U partitions significantly into the metallic phase at increasing temperatures. This may be due to a decrease in U valence from 4+ to 2+ in high-pressure silicate melts, which our data supports. However, K and Th do not exhibit a similar change in behavior at these conditions, and this may drive fractionation between U and Th in the deep mantle. At the most extreme conditions of core formation, enough U could exist in the core to produce up to 4.4 TW of heat 4.5 billion years ago. Potassium could produce much less heat than U early on (< 1 TW), and due to its short half-life, would have decayed away much faster. While this energy source is significantly greater than was previously thought to be possible, it is likely not enough to explain the presence of the geomagnetic field early in Earth’s history. I have also completed a synchrotron-based study to determine the phase behavior and equations of state of UO2 and ThO2. ThO2 undergoes a phase transition from the fluorite- type structure (thorianite) that is stable at ambient conditions to the previously identified cotunnite-type structure around 19 GPa and 1500 K. It remains in the cotunnite-type phase up to 60 GPa and 2500 K. UO2 undergoes several solid phase transitions at high pressure. The fluorite-type (uraninite) to cotunnite-type transition occurs around 20 GPa above 1100 K. At around 35 GPa, a new phase emerges; this phase has been indexed to a tetragonal crystal structure. Finally, at 80 GPa and above, UO2 undergoes another phase transition or dissociates into two separate oxides. This understanding of the phase behavior of the simplest actinide-bearing minerals provides insight into the mineralogical hosts for these radioactive elements, as well as other large cations, in the Earth’s deep mantle.