  We are entering an era where the numerical construction of generic spacetimes
is becoming a reality. The use of computer simulations, in principle, allows us
to solve Einstein equations in their full generality and unravel important
messages so far hidden in the theory. Despite the problems still found in
present applications, significant progress is being achieved in a number of
areas where simulations are on the verge of providing useful physical
information. This article reviews recent progress made in the field, paying
particular attention to black hole spacetimes and discuss open problems and
prospects for the future.
