Polygamy is the state of being married to more than one person at the same time. It exists in several forms, most of which fall under the umbrella of consensual nonmongamy. When a woman has multiple husbands the practice is technically polyandry while when a man has multiple wives the practice is technically called polygyny. A marriage that contains multiple husbands and wives is generally referred to as an example of polyamory. Society at large, however, tends to lump all of these together and refer to them as polygamy.
More About Polygamy
There are many places in which the practice of polygamy is not legal and people with more than one spouse are labeled bigamists. Globally, polygamy is fairly common with polygyny being more often practiced than polyandry. Polygamy remains illegal in the United States. Many believe that it is fundamentalist religious sects that are fighting for the legalization of the practice, however there is also a thriving polyamorous community whose lifestyle is being driven underground by current laws.