The excitation and dissipation of tides strongly influences the evolution of most close binary systems, from planetary systems to compact object binaries. Despite the fact that the theoretical framework for understanding tides in binary systems is well over a century old, many of the observed orbital properties of close binaries are still not well understood. In this talk I will describe ongoing work that attempts to go beyond the standard linear theory treatment of tides in stars, focusing on solar-type stars with either stellar or planetary (hot Jupiter) companions. I will describe how nonlinear interactions dramatically modify both the excitation and damping of resonantly excited internal gravity waves in stars: the linear approximation used in previous investigations does not hold. I will conclude by discussing the implications of these effects for the orbital properties of solar-type binaries and for the orbital decay of Jupiter-mass planets around sun-like stars.