Abstract: Cosmic Microwave Background (CMB) observations traditionally assume an isotropic and homogeneous infinite Universe. However, a growing number of large-scale anomalies and dipoles in the literature suggest the need to revisit these assumptions. A physically well-motivated explanation for these anomalies is the impact of the Universe's topology. Even in a flat Universe, its topology can introduce anisotropic correlations in the CMB. In this talk, I will introduce the concept of Cosmic Topology and present the recent and ongoing work of the COMPACT collaboration on the observational effects of the Universe's topology. I will discuss the specific, testable predictions for the CMB and other cosmological observables, focusing on how advancements in data analysis and future polarization measurements can reveal the global shape of the Universe.