Binary stars with small orbital separations become tidally distorted, with a rich and unanticipated diversity of resulting effects. Pulsations of tidally distorted stars can become ``tidally trapped,” exhibiting amplitude modulation over the orbital period that creates new opportunities for asteroseismology. In other cases, stellar pulsations may tidally interact with the companion, causing an unusual “inverse” tidal evolution that pumps the eccentricity and spin-orbit misalignment of the stars. When a tertiary companion is present, the competing effects of spin and orbital precession can trap the system in a bizarre Cassini state characterized by extremely slow stellar rotation. Finally, tidally excited pulsations can become locked into resonance with the orbital motion, causing greatly enhanced tidal dissipation, with implications for systems ranging from Saturn’s moons to binary black holes.