  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).
