One of the most important techniques in the ultracold atom toolbox is the optical lattice: a periodic scalar potential formed from standing waves of light. Optical lattices are central to the use of atomic gases to explore strong-correlation phenomena related to condensed matter systems. I shall describe how optical coupling of internal states of an atom can be used to create new forms of optical lattice, which cause neutral atoms to behave as charged particles in a strong effective magnetic field. The resulting Lorentz force will twist the trajectories of atoms into tight circles, completely altering the collective behaviour of the gas. I shall explain the origin of this Lorentz force, and the possibilities these lattices offer to explore novel topological many-body phases using ultracold gases.