Tides significantly impact the structure, evolution, and fate of many types of close binary systems, including short-period exoplanets, stellar binaries, and coalescing binary neutron stars. In many of these systems, the tide’s amplitude is so large that it cannot be treated as a small, linear perturbation to the background star. In this talk, I will show that nonlinear effects can greatly enhance the rate of tidal dissipation and thus the rate of binary evolution. As examples, I will describe how nonlinear tides influence the orbital decay of hot Jupiters and the gravitational-wave signal of coalescing binary neutron stars and white dwarfs. I will also discuss the nonlinearity of oscillation-modes in solar-like stars, which are excited by turbulent motions within the convective envelope. The rich oscillation spectra observed by space missions such as Kepler and TESS have revolutionized the field of asteroseismology and yielded a wealth of information about the internal and global properties of thousands of stars.