  We discuss the hyperboloidal evolution problem in general relativity from a
numerical perspective, and present some new results. Families of initial data
which are the hyperboloidal analogue of Brill waves are constructed
numerically, and a systematic search for apparent horizons is performed.
Schwarzschild-Kruskal spacetime is discussed as a first application of
Friedrich's general conformal field equations in spherical symmetry, and the
Maxwell equations are discussed on a nontrivial background as a toy model for
continuum instabilities.
