Important gaps remain in our understanding of the alteration of uranium deposits and nuclear materials, and we can gain insight into those processes by examining the structure and stability of U minerals. Natural processes leading to formation of novel uranyl structures motivate my work, and supplement our observations of the crystal-chemistry of uranium. This dissertation contains descriptions of five new uranium minerals from localities around the world. I address their relationship to the broader family of uranyl structures, and explore crystal-chemical drivers for their formation. Leószilárdite and leesite are found in the Red and White Canyon regions of southern Utah, USA. Leószilardite is the first sodium and magnesium uranyl carbonate known, and is rare owing to its high solubility. Leesite is a K-bearing member of the schoepite family – some of the first phases to form during alteration of UO2. Its description has implications for the nuclear fuel cycle, particularly the uptake and incorporation of 137Cs into its structure. I describe two Pb-bearing uranyl oxide hydroxyl hydrate (UOH) phases, gauthierite and shinkolobweite, from the Shinkolobwe mine in Africa, which help decipher the complex paragenesis of UOH minerals. Gauthierite contains a novel sheet of uranium atoms, revealing crystal-chemical influences for the formation of specific sheets, and shinkolobweite is an exceptionally rare UV and UVI phase with a modulated structure. Little is known about the formation of mixed valent U minerals, but paragenetic relationships are revealed using the charge deficiency per anion (CDA) measure. The new mineral descriptions presented within culminate with the uranyl carbonate mineral ewingite. Using single-crystal synchrotron X-ray data I show that its structure contains a ~2.3 nm cluster, and is the largest and most structurally complex known on Earth. Ewingite challenges geochemical models for uranium transport and understanding the role of complexity in minerals.Lastly, single crystal neutron diffraction of the uranyl peroxide nanocluster U60 resolves the positions of H atoms and Li+ cations in its structure, and their dynamics are probed by Magic Angle Spinning NMR spectroscopy experiments. Our results indicate hexagonal pores in the U60 cage rapidly shuttle Li and H2O molecules from inside and out, even in the solid state.