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Spintronics, a class of devices that exploit the spin properties of electrons in addition to the charge properties, promises the possibility for nonvolatile logic and memory devices that operate at low power. Graphene is a material in which the spin orientation of electrons can be conserved over a long distance, which makes it an attractive channel material in spintronics devices. In this dissertation, the properties of graphene that are interesting for spintronics applications are explored. A robust fabrication process is described for graphene spin valves using Al2O3 tunnel tunnel barriers and Co ferromagnetic contacts.  Spin transport was characterized in both few-layer exfoliated and single-layer graphene, and spin diffusion lengths and spin relaxation times were extracted using the nonlocal spin valve geometry and Hanle measurements. The effect of input-output asymmetry on the spin transport was investigated.  The effect of an applied drift electric field on spin transport was investigated and the spin diffusion length was found to be tunable by a factor of ~8X (suppressed to 1.6 µm and enhanced to 13 µm from the intrinsic length of 4.6 µm using electric field of ±1800 V/cm). A mechanism to induce asymmetry without excess power dissipation is also described which utilizes a double buried-gate structure to tune the Fermi levels on the input and output sides of a graphene spin logic device independently. It was found that different spin scattering mechanisms were at play in the two halves of a small graphene strip. This suggests that the spin properties of graphene are strongly affected by its local environment, e.g. impurities, surface topography, defects. Finally, two-dimensional materials beyond graphene have been explored as spin channels.  One such material is phosphorene, which has low spin-orbit coupling and high mobility, and the interface properties of ferromagnets (cobalt and permalloy) with this material were explored.  This work could potentially enable spin injection without the need for a physical tunnel barrier to solve the conductivity mismatch problem inherent to graphene.