Space metrology and space-time warping

Gravity is the most mysterious of all interactions, even though it was the rst to be formalized. It is the only interaction for which the equivalence principle holds between the gravitational charge and the inertial mass, with a num- ber of far reaching consequences. In addition, gravity is so weak with respect to all other interactions that it is not surprising that most precise tests of general relativ- ity are performed in outer space. General relativity tells us that gravity concerns the curvature of space and time, so testing gravity means applying metrology at is best. In this review I discuss some of the most important tests of general relativ- ity performed in space, starting from the observables, discussing the experimental methods, the current results and some of the the future developments.