Recent discoveries regarding current-induced spin-orbit torques produced by heavy-metal/ferromagnet and topological insulator/ferromagnet bilayers provide the potential for dramatically improved efficiency in the manipulation of magnetic devices. However, spin-orbit torques have an important limitation – in the vast majority of samples, the current-generated spin direction is required by symmetry to lie in the sample plane and perpendicular to an in-plane applied current, i.e., a Rashba-like symmetry. This means, for example, that spinorbit torques can drive the most current-efficient type of magnetic reversal (antidamping switching) only for magnetic devices with in-plane anisotropy, not the devices with perpendicular magnetic anisotropy that are needed for highdensity applications. In this dissertation, I outline a promising approach for reducing those symmetry requirements: using a single crystalline spin-source material with low structural symmetry to alter the symmetry constraints of the generated spin-orbit torques.