Atoms confined to a 3D optical lattice offer both a powerful tool for quantum sensing, and a means to explore interacting quantum many-body systems. While the low-energy properties of such systems are well-captured by the canonical Fermi-Hubbard model from condensed matter physics, commonly employed tools in sensing such as laser driving can dramatically change the microscopic properties. I will explore the effects of one such phenomenon, light-induced spin-orbit coupling, on the non-equilibrium properties of fermionic atoms in a 3D optical lattice. I will describe the anisotropic superexchange spin interactions experienced by the atoms, and discuss applications for generating entangled states useful to quantum sensing. Going beyond effective spins, I will also describe some more exotic kinetically constrained Hubbard-style models that can emerge, discuss their thermal equilibration properties, and touch on prospective applications such as quantum simulation of synthetic magnetic fields. Finally, I will go over recent experimental observations of these predictions.