Homogeneous and isotropic Gaussian fields are fully described by their 2pt correlation function. However, these assumptions are not always met in the study of cosmological fields such as the Cosmic Microwave Background (CMB) or the Large Scale Structure (LSS). In order to test these assumptions, and extract further information if possible, the Cosmology community has adopted a rich variety of statistics. Among them, Minkowski Functionals (MFs) are powerful statistical tools used to describe the morphology of observable fields, and are sensitive to deviations from non-Gaussianity. They have been widely studied in the Statistics literature, as well as in Cosmology, with diverse applications such as blind tests of non-Gaussianity, enhancing parameter constraints, or constraining extended cosmological models. In this talk, I will introduce these statistics and highlight recent advancements in applying them to CMB polarization. I will also introduce ‘Pynkowski,’ an accessible public Python package we developed to make these statistics more accessible to the community. In the last part of the talk, I will focus on the assumptions of isotropy and homogeneity, and why they are claimed to be in tension with some observations. I will introduce one of the best motivated theories that could break isotropy and homogeneity, a non-trivial topology of the Universe, and mention some of the latest theoretical results by the COMPACT Collaboration.