This thesis studies periodic variability in large optical sky surveys, focusing on long-period variable sources. A primary challenge in studying these objects is accurately determining their periods. The first part of this thesis addresses this by introducing a set of filters to reliably identify periods of sources in the SDSS S82, which were previously classified as non-variable. Five quasars with plausible periodic variability were identified by applying several criteria to the light curves. These criteria included requiring at least 25 data points, matching periods in the SDSS gri filters within 0.1%, and ensuring good agreement with a simple sinusoidal model. Potential aliases were filtered out by requiring distinct periods and calculated uncertainties that were not multiples of one year. Additionally, Kuiper statistics were used to ensure no significant gaps or clustering of points in each phase light curve. In the second part of this thesis, the focus is on one of the previously detected quasars with the shortest period of 278 days. This quasar is analyzed using new observations of MgII lines and archived SDSS spectra, providing three epochs of MgII observations. The key findings include the discovery that the newly observed MgII line exhibits a double-peaked profile that changes over time. By comparing synthetic magnitudes with photometric data as well as using the PoSKI model, which analyzes emission lines and light curves of candidate supermassive binary black holes (SMBBH), a correlation was found suggesting a closely orbiting SMBBH. The latest release Gaia DR3, included light curves for all objects within a field centered on the Andromeda Galaxy. The final scientific part of this thesis focuses on identifying Mira stars in the M31 galaxy and determining their periods. For the first time, a period-luminosity (PL) relation for Mira variables in the M31 galaxy has been established using Gaia filters. This relation is compared with PL relations for multiple galaxies presented in other works, using 2MASS data. Although the method can be improved, the results are promising and lay the groundwork for future research utilizing Gaia’s light curves for the entire sky.