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Recent observations of gravitational waves represent a remarkable success of our theoretical models of relativistic binaries. However, accurate models are largely restricted to binaries in which the two members have roughly equal masses; for binaries with more disparate masses, modelling is less mature. This is especially relevant for extreme-mass-ratio inspirals (EMRIs), in which a stellar-mass object orbits a supermassive black hole in a galactic core. EMRIs are uniquely precise probes of black hole spacetimes, and they will be key targets for the space-based detector LISA. They are best modelled by gravitational self-force theory, in which the smaller object generates a small gravitational perturbation that reacts back on it to exert a "self-force", accelerating the object away from geodesic motion. For LISA science, we must work to second order in this perturbative treatment. In this talk, I discuss the foundations of self-force theory, its application to EMRIs, and the current status of first- and second-order models.