  In this review we summarize the current understanding of the
gravitational-wave driven instability associated with the so-called r-modes in
rotating neutron stars. We discuss the nature of the r-modes, the detailed
mechanics of the instability and its potential astrophysical significance. In
particular we discuss results regarding the spin-evolution of nascent neutron
stars, the detectability of r-mode gravitational waves and mechanisms limiting
the spin-rate of accreting neutron stars in binary systems.
