There are two types of marriage allowed in normative Judaism, both of them involve a monogamous relationship, and both require the woman to observe niddah laws:
1. Kiddushin marriage: husband acquires relationship with wife by giving ring, husband is the baal (leader of the household), the marriage is only severed by death or a Get.
2. Pilegesh (concubine) marriage: husband does not acquire wife, no Get is required to end, husband is NOT baal.
Authentic (IE non-feminist) halachic principles of kiddushin marriage preclude any “right” to arbitrary divorce on demand by either spouse, and those principles usually invalidate any gittin forced on Jewish husbands. We do not claim that pilegesh marriage should replace all kiddushin marriage. However from the standpoint of halacha, for those Jews who are unable to accept the halachic principles of kiddushin marriage, pilegesh marriage is actually far less problematic than the problems that regularly occur during today’s divorce conflicts under kiddushin marriage.
Pilegesh marriage is an authentic Torah concept that unfortunately has been ignored or suppressed for far too long now in frum communities. A pilegesh marriage offers a type of marriage relationship, that when performed properly, will eliminate the severe problems we are now facing from forced and invalid gittin that lead to adultery and mamzerim.
The article linked here offers an excellent explanation of how pilegesh marriage works.
http://torahhalacha.blogspot.com/search/label/Kiddushin%20Makes%20Problems%20and%20Pilegesh%20Makes%20Hope