Direct observations of gravitational waves will open in the nearfuture new windows on the Universe. Among the expected sources,instabilities of rotating compact astrophysical objects are waited tobe detected with some impatience as this will sign the birth of“gravitational waves asteroseismology”, a crucial way to improve ourknowledge of matter equation of state in conditions that cannot bereproduced in a lab. However, the theoretical work needed to reallyget informations from to-be-detected signals is still quite large, numericalsimulations having become a necessary key ingredient. This articletries to provide a short overview of the main physical topics involvedin this field (general relativity, gravitational waves, instabilitiesof rotating fluids, etc.), concluding with a brief descriptionof the work that was done in Paris-Meudon Observatory by SilvanoBonazzola and collaborators.