In the past several years, a plethora of gravitational wave events have been detected leading to better understanding of binary black holes, binary neutron stars, and neutron star black hole binaries. All of these transient detections have helped us better understand the dynamics of these systems as well as the populations of these objects, but each of these sources was detected with models that neglected eccentricity. Eccentricity is one of several potential markers for determining the formation of binary systems. Detecting gravitational waves from eccentric sources can better our understanding of such systems and help constrain theories about their formation. In the ground-based gravitational-wave regime, most eccentric binary black hole sources will be detected with little to no eccentricity (e0.1), but the lack of eccentricity-based models implemented into current search methods will make detecting such systems difficult. In the pulsar timing array regime, previous implementations of eccentricity-based models proved to be too computationally expensive. Recent developments in eccentric modeling of supermassive black hole binary systems have made it possible to incorporate eccentricity in a search for continuous gravitational waves from eccentric supermassive black hole binary sources. This work details the methods developed to aid in searching for eccentric stellar-mass black hole binary sources in the ground-based gravitational-wave regime and eccentric supermassive black hole binaries in the pulsar timing array regime
