The fundamental laws of physics known to date suggest that equal amounts of matter and antimatter should have been produced, and annihilated, during the Big Bang. Yet, observations show that antimatter is present at most in tiny traces is the Solar System and Milky Way neighbourhood, and that a perfect symmetry between matter and antimatter is ruled out at the scale of the entire Universe. In this seminar I will present a review of the observations that characterise the matter-antimatter asymmetry in the Universe and I will briefly outline some theories that try to explain it. I will conclude by presenting some recent observational results that may indicate cracks in the current paradigm that the Universe has been free of antimatter domains since its early phases.