Numerical simulations of black-hole binaries and gravitational wave emission

We review recent progress in numerical relativity simulations of black-hole (BH) spacetimes. Following a brief summary of the methods employed in the modeling, we summarize the key results in two major areas of BH physics: (i) BHs as sources of gravitational waves (GWs) and (ii) astrophysical systems involving BHs. We conclude with a list of the most urgent tasks for numerical relativity in these areas.