Thanks to the Rossi X-ray Timing Explorer (RXTE), it is now widely recognized that fast X-ray timing can be used to probe strong gravity fields around collapsed objects and constrain the equation of state of dense matter in neutron stars. We first discuss some of the outstanding issues which could be solved with an X-ray timing mission building on the great successes of RXTE and providing an order of magnitude better sensitivity. Then we briefly describe the Experiment for X-ray timing and Relativistic Astrophysics (EXTRA) recently proposed to the European Space Agency as a follow-up to RXTE and the related US mission Relativistic Astrophysics Explorer (RAE).