Rotating neutron stars have modes that are driven unstable by the gravitational radiation reaction. The r-mode instability converts rotational energy into gravitational radiation and mode energy. When the L=2, m=2 R-mode grows above its parametric instability threshold it excites other near-resonant modes in the star. The nonlinear development of the instability plays an important role in the spin and temperature evolution of the star. The r-mode instability could (1) set the largest angular velocity of accreting neutron stars and (2) spin down newborn neutron star closer to the observed frequencies of young pulsars.