Abstract: Binary neutron star mergers (BNSM) are cosmic collisions of compact stars associated with powerful gravitational-wave and electromagnetic astronomical transients. Multimessenger observations of BNSMs promise to deliver unprecedented insights on fundamental physics questions, including constraints on dense matter models and the production of heavy elements. Detailed theoretical predictions of the merger dynamics are crucial for extracting information from such observations. This talk reviews recent progress on the modeling of BNSMs using simulations in 3+1 numerical general relativity. In the first part, I will discuss predictions for the complete (inspiral-merger-postmerger) gravitational-wave spectrum and their application in gravitational-wave astronomy. In the second part, I will discuss merger remnants and mass ejecta, the mechanisms behind kilonova light and the application of these results to the analyses of multimessenger observations.