The direct detection of the inspiraling gravitational wave signal from the binary neutron star merger GW170817, by LIGO, together with the detection of its electromagnetic counterparts GRB170817A and AT2017gfo, announced the birth of the multi-messenger astronomy era. Numerical relativity, i.e. solving Einstein’s equation with numerical methods to simulate the binary merger process, played a crucial role in the detection of the gravitational wave signal as well as in interpreting the properties of the source. Moreover, the results of numerical relativity studies of binary neutron star mergers are essential for understanding the counterpart electromagnetic observations. In this article, the history and evolution of numerical relativity will be reviewed, as well as its role in gravitational wave detection and interpretation of the observations.