Polyamory

Polyamory is the idea and practice of loving (romantically/sexually/intimately) more than one person at the same time. An important tenet of polyamory is consent and communication; cheating is not considered "polyamorous" as it is done without the consent and often without the knowledge of one or more of the people involved in the relationship.

Polyamorous people come in all sexualities (including asexual), and relationships can have many different shapes and sizes. It is possible for a monogamous person to be involved in a polyamorous relationship if that person is in a relationship with a person who is polyamorous and consents to that person having other relationships.

Guidelines for communication
Many people who are in or starting a polyamorous relationship will lay down rules about if or how a new person can be added to the relationship (or if a person can start outside relationships), practices for maintaining their sexual health, and how to handle practicalities such as interpersonal conflicts and even time management. These ground rules are often revised as needed. Disregarding the ground rules can be considered cheating even if the offending behavior was not a sex act.

Polyfidelity
Polyfidelity is a term used to describe a closed polyamorous relationship, one where the people involved in the relationship aren't looking for any other lovers or sexual partners.