The Quranic permission comes in a passage about orphans and their property, and it is conditional twice over. A man may marry two, three or four, and then the verse says that if he fears he will not deal justly he should marry one. A later verse in the same chapter says that a man will not be able to deal equally between wives however much he wishes to, and asks him at least not to leave one suspended.
Classical jurisprudence read the required justice as covering the things that can be measured, maintenance, housing and the division of nights, and read the impossible equality as concerning affection, which nobody can command. On that reading the permission stands with a practical condition attached, and the courts enforced the measurable part.
Modern reformist argument put the two verses together and drew a different conclusion: that a permission granted on a condition the text elsewhere says cannot be met amounts to a strong preference for one wife. Muhammad Abduh in Egypt is the figure most associated with the argument, and it has been contested within the tradition ever since. Legislation went further in places. Tunisia prohibited plural marriage outright in its personal status code of 1956, and a number of other states require judicial permission, notice to the existing wife, or proof of means.
Beyond the scriptural traditions, polygyny has been widespread as custom rather than doctrine across much of Africa, parts of South Asia and many Indigenous societies. The atlas records it as one arrangement among several and takes no position for or against it.