  Solving Einstein's equations precisely for strong-field gravitational systems
is essential to determining the full physics content of gravitational wave
detections. Without these solutions it is not possible to infer precise values
for initial and final-state system parameters. Obtaining these solutions
requires extensive numerical simulations, as Einstein's equations governing
these systems are much too difficult to solve analytically. These difficulties
arise principally from the curved, non-linear nature of spacetime in general
relativity. Developing the numerical capabilities needed to produce reliable,
efficient calculations has required a Herculean 50-year effort involving
hundreds of researchers using sophisticated physical insight, algorithm
development, computational technique and computers that are a billion times
more capable than they were in 1964 when computations were first attempted. My
purpose is to give an accessible overview for non-experts of the major
developments that have made such dramatic progress possible.
