  This talk reports on recent progress toward the semiglobal study of
asymptotically flat spacetimes within numerical relativity. The development of
a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has
rendered possible the application of Friedrich's conformal field equations to
astrophysically interesting spacetimes. As a first application, the whole
future of a hyperboloidal set of weak initial data has been studied, including
future null and timelike infinity. Using this example we sketch the numerical
techniques employed and highlight some of the unique capabilities of the
numerical code. We conclude with implications for future work.
