Polygyny is the main form of polygamy, when one man is married to several women at one time. This doesn’t involve a strict definition of marriage, it could involve being legally married to only one woman, but living together, as spouses, with that woman as well as others. In countries where polygamy is against the law, communities that practice it manage to do so by either not formally marrying additional wives, or marrying and divorcing each one in turn.
This way the women take on the man’s last name, and continue to live with him, but are not technically simultaneously married.
Because Common Law steps in when partners cohabitate for long periods of time and even have children together, these families are in fact breaking the law. One of the major problems then becomes that these wives do not share the rights and protections that a monogamously married woman has.
Other problems associated with polygyny are that girls are often forced to marry at an early age, which can constitute statutory rape if they are below the legal age in their state to consent to sex. Often they are.
Whether females who partake in polygyny are sexually satisfied is each lady’s call, but the conservative nature of the known communities denies us access to this information.
Polygyny as a traditional practice is still followed today in the Middle East and Central and Southern Africa. It is also a more recently instituted practice among Mormon fundamentalist groups in the western parts of North America.