Thanks to the Rossi X-ray Timing Explorer (RXTE), it is now widely recogniz
ed 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 n
eutron stars. We first discuss some of the outstanding issues which could b
e solved with an X-ray timing mission building on the great successes of RX
TE and providing an order of magnitude better sensitivity. Then we briefly
describe the 'Experiment for X-ray timing and Relativistic Astrophysics' (E
XTRA) recently proposed to the European Space Agency as a follow-up to RXTE
and the related US mission 'Relativistic Astrophysics Explorer* (RAE),