Polygamy has been an issue in Anglo-American jurisprudence for a long time. It first became a secular criminal offense in this legal tradition in 1604.
Already in Anglo-Saxon times, England condemned polygamy as a serious moral offense. But until 1604, it was left to church courts to punish polygamists using spiritual punishments. In 1604, however, Parliament enacted the Polygamy Act that made polygamy a capital crime, punishable by secular courts. Both individual victims of desertion or double marriage as well as church or state officials could initiate indictment of parties for polygamy. Other interested parties also had standing to press polygamy claims.
Thousands of polygamy cases came before the criminal tribunals of England, not least the famous Old Bailey, which heard more than 500 such polygamy cases under the 1604 Act.
Convicted parties faced punishments ranging from fines and short imprisonment, to transportation to a penal colony or execution orders, though almost all those convicted for a capital felony successfully pled benefit of clergy. The vast majority of polygamy cases were brought against men, and they were punished far more severely than women if convicted.
The 1604 Polygamy Act -- while eventually replaced by Acts of Parliament in 1828 and 1861 that made felony a non-capital crime -- was a model for the common law world.John Witte Jr., Prosecuting Polygamy in Early Modern England (2016). Hat tip: Legal Theory Blog.