Bigamy is the practice of being married to two people at the same time. In the event of bigamy, the second marriage is typically declared void. An annulment may be issued by a judge. The first marriage, in this case, is not legally affected. While bigamy is technically a crime in the US, it is often not prosecuted unless it is perpetrated in conjunction with another felony such as fraud.
More About Bigamy
In the US, the legality of bigamy is not affected by the consent of the parties involved. This is a point of contention in polygamous and polyamourous relationships.
It is possible for one to commit bigamy unintentionally such as in the case of a spouse that was thought to be deceased and is found to be alive or a divorce that was unknowingly not finalized.