Double compact objects, such as double white dwarfs, neutron star binaries and black hole binaries, give rise to observational phenomena which are important for studying a wide variety of astrophysical problems (e.g., gravitational radiation, gamma ray bursts). We use the population synthesis binary evolution code StarTrack to evolve our entire stellar population, and assess the resulting physical characteristics and formation histories of these compact binaries. This seminar will consist of two parts: After a brief introduction, I will first discuss the Galactic population of double white dwarfs and the impact which the gravitational radiation signal arising from these binaries has on the future space-based gravitational wave observatory LISA. Then, on behalf of my PhD advisor Krzysztof Belczynski, I will give a brief overview of double compact binaries consisting of NS-NS, BH-NS and BH-BH, both from observational and theoretical perspectives. I will also present predictions for merger detections with LIGO, and discuss what astrophysics may be learned from such detections.