  In this review article, we present the main results from our most recent
research concerning the oscillations of fast rotating neutron stars. We derive
a set of time evolution equations for the investigation of non-axisymmetric
oscillations of rapidly rotating compact objects in full general relativity,
taking into account the contribution of a dynamic spacetime. Using our code,
which features high accuracy at comparably low computational expense, we are
able to extract the frequencies of non-axisymmetric modes of compact objects
with rotation rates up to the Kepler limit. We propose various universal
relations combining bulk properties of isolated neutron stars as well as of
binary systems before and after merger; these relations are independent of the
true equation of state and may serve as a valuable tool for gravitational wave
asteroseismology. We also present an introductory example using a Bayesian
analysis.
