Classic monogamy—when people married as (at least in theory) virginal teenagers and remained sexually exclusive through their entire lives until one died and the other became celibate -- is no longer the norm in many industrialized nations. Longer life-spans, increasing independence for women, and relaxing sexual mores mean that many people in industrialized nations now prefer serial monogamy, in which people couple exclusively for a time before breaking up and then re-coupling exclusively with someone else.
Not only are we living long enough to get bored with each other, we can also control our reproduction so that sex and babies do not necessarily go together any more. All of this means that people have more choices and more time to test them out. The popularity of divorce indicates that marriage is not a lifelong contract for about half of the people who try it (at least in the US), and cohabitation without being married further dilutes the primacy of marriage.
Some married people create agreements that allow them to have sex with other people. Swingers have recreational sex for fun and sexual novelty, polyamorists have emotionally intimate relationships with more than two people, and lots of folks have monogamish relationships in which they can have occasional sexual trysts with other people either independently or as a couple.
Probably most importantly, many young people dating each other today—especially in the college hook-up culture—no longer expect monogamy to be the unspoken standard. Hooking up with someone does not mean that the pair are dating or exclusive, and reaching that decision requires a define the relationship talk (DTR) to negotiate sexual exclusivity. Once monogamy is something that everyone has to negotiate, it has lost its hold on cultural primacy. This does not mean that everyone will be swingers and polyamorous— the simplicity of monogamy will continue to appeal to a lot of people. But it does mean that monogamy is no longer the only real option, and people will increasingly expect to negotiate levels of sexual exclusivity with a number of lovers across their lifetimes.
In addition to sexual variety, the benefits of non-monogamy are varied enough to be appealing to many people. Pooling the resources of multiple partners allows for more money, love, sex, and assistance for everyone, plus the added bonus of more sleep for families with infants. Kids growing up with multiple adults caring for them get lots more attention and help with homework. People in non-monogamous relationships don’t have to be alone if one of their partners is traveling, they break up with a partner, or one of their partners dies, they can still rely on the others for emotional comfort and companionship. Rather than erasing monogamy, non-monogamies will become increasingly popular options in the years ahead.