  Gravitational radiation (GR) drives an instability in certain modes of
rotating stars. This instability is strong enough in the case of the r-modes to
cause their amplitudes to grow on a timescale of tens of seconds in rapidly
rotating neutron stars. GR emitted by these modes removes angular momentum from
the star at a rate which would spin it down to a relatively small angular
velocity within about one year, if the dimensionless amplitude of the mode
grows to order unity. A pedagogical level discussion is given here on the
mechanism of GR instability in rotating stars, on the relevant properties of
the r-modes, and on our present understanding of the dissipation mechanisms
that tend to suppress this instability in neutron stars. The astrophysical
implications of this GR driven instability are discussed for young neutron
stars, and for older systems such as low mass x-ray binaries. Recent work on
the non-linear evolution of the r-modes is also presented.
