There are many types of non-monogamous relationships. Most dating relationships technically begin as open, when both people are still determining their compatibility. Some couples choose to keep their relationships casual longer than others. This can work as long as both people agree and one does not end up falling hard for the other and secretly wanting a commitment. This can (and often does) get tricky! In more established, committed couples, an open relationship is one in which there are two primary partners, and they have an agreement that allows each to have outside affairs, but share a commitment to remaining with their primary partner in a loving relationship.{relatedarticles}
There are other, alternative versions of open relationships that are more unconventional. For example, polyamory, in which the relationship involves 3 or more people in a loving, committed bond. This is much like the plural marriage found in some sects of Mormonism and other cultures around the world. In other kinds of arrangements, some couples choose to have their sexual adventures together, whether among friends or at swinging clubs. Scared yet? These alternative lifestyles are definitely not for everyone, and nobody should be pressured into sexual arrangements that go against their faith or morals. Ultimately, it's up to you. But whatever you choose, be sure to set ground rules.