How thermal physics arises in isolated quantum many-body systems has emerged as a central question in condensed matter physics. Its mechanism is additionally linked to the understanding of many other key puzzles, from the behavior of cold atoms in optical lattices to the black hole information paradox. In this seminar, I will take a step forward by investigating the role of conservation laws (including energy conservation) in quantum thermalization. In particular, I will focus on a crucial ingredient of thermalization: the scrambling, or delocalization, of quantum information. I will show that while energy conservation alone does not affect information scrambling, the existence of symmetries generally leads to a decreased amount of scrambled information. I will further discuss the implications of our theory in quantum chaos and black hole physics. In particular, I will show why black holes may not be the best information scrambler in nature. I will end the talk with an outlook of some exciting directions, both theoretical and experimental, in this interdisciplinary field.