Most societies in the world permit polygyny (though most men in these societies do not practice it).
Polygyny presents a logical problem: societies are far more likely to have an excess of men than an excess of women...so where do the women for polygynous marriage come from?
Next: Marriage and age
Polygyny has been in steady decline for more than 100 years (and perhaps for far longer than that). However, although for fairly obvious logical reasons, there has never been a society in which most men practiced polygyny, it was accepted as a permitted practice in the vast majority of the world's societies. We often think of Europe as strongly supporting monogamy but the question of the permissibility of polygyny wasn't settled there until about 1,000 years ago. Many medieval rulers had multiple wives (the Merovingian kings of France as well as medieval Irish kings were notorious for it).
Polygyny is frequently associated with Islam, which does allow men to have up to four wives. However, currently fewer than 1% of Muslim men live with more than one spouse in Afghanistan, Pakistan, Bangladesh, Iran and Egypt – all countries where the practice is legal at least for Muslims. This is typical of other Muslim countries as well.
The two countries with the largest percentage of people living in polygynous families are Burkina Faso and Mali, both in Africa, and both countries where I happen to have lived and worked.