We propose a research program to explore the implications of compact binaries, with emphasis on pulsar binaries, for gravitational-wave astronomy. Interest in compact binaries derives not only from an intrinsic motivation of understanding their origin and evolution in various astrophysical environments, but also from the fact that these are strong sources of gravitational waves. Pulsar binaries, one of the prime targets for ground-based gravitational-wave detectors, form a subgroup of compact binaries. This work will involve (a) a comprehensive study on the empirical properties of Galactic pulsar population and (b) a systematic analysis to constrain theoretical models on binary evolution using the empirical rate estimates relevant to pulsar binaries. Establishing the preferred model parameter space will allow us to explore various types of compact binaries with better constraints. This work can be expanded to study statistics of gamma-ray bursts, which are also strong sources of gravitational waves. As one of the short-term projects, we will compare observational properties of gamma-ray bursts with theoretical predictions. This study will provide a unique tool to quantify uncertainties in theoretical assumptions on the formation and evolutionary channels of compact binaries, as well as to calculate more reliable rate estimates for the gravitational wave detection for the current and future detectors.