Transients (転光生) are beings that came from other worlds summoned to Tokyo. The exact mechanism of how each transient is summoned to Tokyo is not fully known but it is connected to the Game and a wish that keeps them anchored to the city. The list of Transients can be seen here, though it also includes the native Humans; unreleased Transients here.
There are currently 23 Worlds taking part in the Game and the transients are beings such as gods, goddesses, folk heroes, fairytales of various cultures summoned to Tokyo in an age that they see themselves as, if a being sees themselves more mature or immature, they'll be summoned as being those ages.
For them to be properly summoned to Tokyo, they must first establish a bond with a native Tokyo human that participates in the Game via the app on their phone. The bond is usually formed when the transient and the human have a want or wish that is similar or coincides with one another. The transient will then materialized near their summoner. A special mark usually referred to as a Summon Emblem, will appear on the summoner and will appear on the transient if the summoner comes into contact with them so as to identify who summoned the transient and as proof of their pact.
The transients and native humans, are assigned specific rules and roles with which dictates what their ability is and how it can be presented. Two or more transients can have the same rule or the same role but never both. Beings with the same rule and role as another that's already in Tokyo are barred from entering until that unit is removed or no longer has the same rule or role.
Though not every being from different worlds can enter Tokyo. Even if they meet the requirements of being able to enter Tokyo, the Game is highly sensitive to beings that could pose a problem to its structure and so they are placed in an unknown space and their Sacred Artifacts are instead given to their summoners. If ever a contradiction occurs that involves the Sacred Artifacts, power will then surge to the original owner of the artifact and often cause them to go on a rampage; if the sacred artifact is in the hands of a native human, it will often cause an Exception to appear taking shape of the original holder.
Stray transients are those beings that are summoned to Tokyo but have lost their bond or pact to their summoner and have yet to establish a new one. If they do not establish a new pact, then they are removed or unsummoned from the game.
A Representative is a transient that represents the world they come from. They are often those that are the most powerful of their respective worlds or those that maintain its perpetuity. The Representatives also have a special connection to Protagonist.
Though not technically a Transient, the 23 worlds each have a being that was exiled from it and their selves were fused together and placed in a single vessel called the Protagonist that was summoned to Tokyo at the start of the game.