Research on quantum entanglement is a dynamically developing trend of modern theoretical physics, which often unifies concepts in field theory, many-body physics, thermodynamics and quantum information theory. In this context, one of the most studied features are "area laws". These laws provide limitations on the strength of possible entanglement between two or more domains (sub-systems) in local models. Historically, area laws emerged first as quantum field theory explanation of the Bekenstein-Hawking entropy formula. In recent years, however, there has been more focus on the role of these laws in the theory of universality classes, equilibration and thermalization, and also in the development of new numerical ansatz states. In the talk, I will present a short overview about this subject and summarize also my results in the last years.