The Compton Spectrometer and Imager (COSI) is an upcoming NASA Small Explorer satellite mission designed to survey the soft gamma-ray sky and provide unprecedented insights into the extreme Universe. Our research program, "COSI: simulation and data analysis of relativistic jet emission," focuses on evaluating the instrument's potential to observe blazars and Gamma-Ray Bursts (GRBs). By conducting comprehensive simulations of the soft gamma-ray emission originating from these highly energetic astrophysical phenomena, our team is assessing the feasibility of using COSI to detect and characterize their relativistic jets.