  We review ways in which observations of the changing periods of pulsating
variable stars can be used to detect and directly measure their evolution. We
briefly describe the two main techniques of analysis -- (O-C) analysis and
wavelet analysis -- and results for pulsating variable star types which are
reasonably periodic: type I and II Cepheids, RR Lyrae stars, beta Cephei stars,
and Mira stars. We comment briefly on delta Scuti stars and pulsating white
dwarfs. For some of these variable star types, observations agree approximately
with the predictions of evolutionary models, but there still exist significant
areas of disagreement that challenge future models of stellar evolution. There
may be a need, for instance, to include processes such as rotation, mass loss,
and magnetic fields. There may also be non-evolutionary processes which are
contributing to the period changes.
