The 4f and 5f electron states from the lanthanide (La - Lu) and actinide (Ac - Lr) elements area deep reservoir for novel physics. A variety of emergent states are seen in different f-element containing materials including complex magnetism, strong hybridization between the f and conduction electron states, unconventional superconductivity, and the coexistence of magnetism and superconductivity. The f-state also has the potential to impact other fundamental characteristics such as the crystal structure, melting temperature, and durability of a material, and this is especially true for actinide elements. Indeed, it is these combined behaviors that cause f-element materials to be so useful in everyday life where many technologies depend on them. Computers and cell phones contain most of the lanthanide elements, while actinide materials help generate power. New materials (e.g., topological insulators, thermoelectrics, and unconventional superconductors) that contain f-elements are synthesized every day and may lead to further advancements like quantum computers, more efficient energy storage, and more economical power generation and transfer. In this dissertation, we present results from studies of several distinct families of f-electroncompounds including, (i) the growth and characterization of an europium{based compound that forms in the ubiquitous ThCr₂Si₂ structure, (ii) a new uranium containing high entropy alloy that exhibits superconductivity at low temperatures, and (iii) a study of the first NpTe₁.₇₅ single crystals, which are related to the recently discovered 'Lazarus' superconductor UTₑ₂. For (i), we find that changes in the immediate environment around an f state atom creates different magnetic ground states and field induced effects. In (ii) we show that actinide elements can be incorporated into high entropy alloys, and note (given the physical strength and chemical robustness of high entropy alloys) that such inclusion may open the way towards new and safer nuclear waste forms. Additionally, the high critical field superconductivity is explored. Finally, our work on NpTe₁.₇₅ reveals its structure and bulk magnetic properties, which we contrast with those of UTₑ₂. This work opens paths towards producing orthorhombic NpTe₂ which might have similar properties to orthorhombic UTₑ₂. Taken together, each of these studies show how the interplay between crystal structure and the f-state can influence material properties, further opening up materials study, where it remains an ongoing challenge to understand how to systematically produce interesting behaviors in these materials.
