The subject of this work is the compositions of asteroids and meteorites. Studies of the composition of small Solar System bodies are fundamental to theories of planet formation. Meteorites, samples available for analysis in the lab, help constrain the timeline and conditions in the early Solar System. Asteroid reflectance spectra help define the links between asteroids and meteorites. Studies of the spectral types and sizes of asteroids test dynamical models. These studies also inform assessments of the impact hazard of near-Earth asteroids and the prospects of mining asteroids for commercial resources. Observational work is reported. The visible (~0.55 - 0.90 μm) reflectance spectra of 18 near-Earth asteroids (NEAs) and 3 Main Belt asteroids have been obtained with the 1.5-meter+FAST spectrograph at Mt Hopkins, AZ. The obtained spectra were The M4AST online spectral classification tool was implemented but has considerable limitations. We report preliminary spectral classifications. A database of meteorite minerals is presented. A literature review was performed and a uniform database containing 66 meteorite minerals was compiled, of which 14 were later found to occur on Earth and 20 were later synthesized. 16 mineral properties are reported for each meteorite mineral, where available. The distribution of meteorite minerals across different meteorite groups is explored. A database of iron meteorite trace element abundances is presented. A literature review was performed and a uniform database containing 708 iron meteorites was compiled. 16 trace elements (Cr, Co, Cu, Ga, Ge, As, Sb, W, Re, Ir, Pt, Pd, Rh, Ru, Os and Au) are reported for each iron meteorite, where available. Mining metallic asteroids for platinum is explored. Iron meteorites with high PGE concentrations can be effectively selected with Ni abundance. Laser ablation, x-ray fluorescence and Ɣ-ray spectroscopy methods for determining, statistically, the Pt content of a particular asteroid are discussed.