Earthquakes are complicated processes varying in time, space and magnitude. The occurrence of a major earthquake event called mainshock is preceded and followed in time by diminishing seismic activities known as foreshocks and aftershocks respectively. The process of identifying mainshocks, aftershocks, and foreshocks in a given earthquake catalog is known as declustering the catalog. Declustering is a difficult problem which has no unique solution. The majority of the research efforts focus mainly on declustering earthquakes in a small region. We are focusing on declustering all the earthquake events on the entire globe from 1973 to 2018 with magnitude greater than or equal to 5.0. In this thesis, we explore two different approaches. In the first approach, we extend the nearest neighbor decluster by creating a network graph of earthquakes and categorizing them. In the second approach, we use the point process model known as Epidemic Type AfterShock (ETAS) model to decluster the global catalog.