I'm into it... My last girlfriend, who passed away last year, was finally letting herself live the poly life. I was one of her partners. I had been in another one previously in Austin years ago. It's always the other person who is with more than one person, never me. I'm just not lucky enough.
Polygamy is different than polyamory. Polygamy is typically one man = several women, in marriage, and polyamory doesn't necessarily have to be defined by marriage. In a lot of cases, there's no one married, or there might be two people married in an open relationship, each person having at least one other unmarried partner (or that second person might even been married to someone else). AS you can see, this is NOT swinging, nor is it sleeping around. Even such poly "families" have boundaries, in that the partners may not add other people to the family in that there is "enough." That is beside the point for polyamory.
Polyamory describes a person loving more than one person in an intimate way (and it doesn't necessarily have to be sexual. It could also be emotional, or physically close without the sex, even). This differs from cheating in that the involved people know about each other, and might even be friends all living in the same house together. I lived with such a family for two months while I was recovering emotionally from a bad situation with a roommate situation. There are many examples of three under the roof with a child or more. All three help out in raising them, taking the load off all of them in the long run.
Thing about this is, if there are any insecurities or hangups about something, any nagging feelings, especially jealousy, these can get magnified big time over time. Communications become even more important because this involves EVERYONE in the group. It is so crucial for the success of the relationship. Honesty is also a necessary trait in these relationships as in monogamous relationships.
I'm hoping that this is a natural outgrowth of the understanding of human nature over time and shedding the artificial restrictions of society. I feel like those of us who are poly have been robbed of so many potential partners because of their upbringing. You have to find poly groups in the area you live in, and you might even have to move to more poly-friendly areas, unless you're willing to hold off the mono-zombies.