The subject of this thesis is the analysis and modeling of the active galactic nucleus PKS 1510-089. The aim is to present a thorough background of active galactic nuclei combined with the analysis and modeling of a specific active galactic nucleus. The results will then be  linked to previous research and theories about active galactic nuclei. The data used in the analysis were retrieved from the Fermi Gamma-ray Space Telescope. A light curve analysis that extended over 12 years provided knowledge about variability and presented four interesting flaring periods. The four periods underwent a spectral analysis, and the results showed that a log parabolic curvature could best describe all four periods. The last step before the modeling was to create spectral energy distributions for all four periods to retrieve spectral points from wavelengths other than those available from Fermi. Unfortunately, there were only sufficient data for one period. That period was later used in the modeling and resulted in a well-fitted external Compton model, which was compared, with relatively good results, with previous research.