The recent detections of gravitational waves from merging black holes and neutron stars have established gravitational waves as a new cosmological messenger and opened remarkable opportunities for probing the nature of gravity and matter in unexplored regimes. Extracting the rich science content of these gravitational-wave signals relies on cross-correlating the data with theoretical template models, which must be highly accurate and efficient to generate. I will describe my recent work in developing such models using analytical methods and their connection to the nonlinear regimes accessible to numerical relativity simulations. I will also discuss the importance of modeling for identifying the key characteristic parameters that link gravitational wave signatures to fundamental properties of the compact objects and for deriving new insights such as on nuclear physics from the observations, and the greater impact from combining information in gravitational waves and electromagnetic counterparts. I will conclude with an outlook onto exciting prospects and urgent challenges as gravitational wave measurements transition from being isolated discoveries to precision physics in the next decade.