Since the first direct detection of a gravitational wave by the Laser Interferometer Gravitational-Wave Observatory in 2015, gravitational waves have become an indispensable tool for studying extreme astrophysical phenomena. To date, eleven of these "ripples in spacetime" have been detected -- ten from merging pairs of black holes and one from two colliding neutron stars. In principle, electromagnetic and neutrino signals can be combined with gravitational-wave data to form a more complete picture of these compact object mergers. In this thesis, we present four studies of gravitational-wave and optical signatures from black-hole and neutron-star mergers. First we describe a technique for emulating expensive simulations of gravitational waveforms using Gaussian process regression, a method for non-parametrically interpolating functions and their uncertainties. The second topic we address is that of the mass ejected from the collision of the two neutron stars that produced the LIGO-Virgo gravitational wave GW170817. We find that the mass dynamically ejected from the merger should enrich its surroundings with heavy r-process elements, suggesting that neutron-star mergers could have played a significant role in the production of heavy elements we see in our solar system. Next we present the analysis and upper limits from the Dark Energy Survey of an independent optical search for kilonovae, the bright optical transients associated with neutron-star mergers. Finally, we describe Dark Energy Camera optical follow-up of black-hole merger GW170814 and the results of that search.