Transmute Monsters are a creation of Metaphyspirit. They are Extra Deck monsters of previously established types with a twist: they're double-sided cards that can vary from being a monster and its evolved form on the same card or are of two different Extra Deck types entirely.
Some Transmutes allow you to access one side or the other immediately, others require you to summon 1 side and transmute to the other later.
Transmute can occur via a card effect or by using the necessary materials to summon the other side in the same Zone the Transmute monster was first summoned in (similar to Gemini Summon).
For example, a Synchro/Xyz Transmute that would flip from its Synchro to its Xyz side would be Xyz-Transmuted. Simultaneously treated as if it was Xyz Summoned and Transmuted. When Transmuting a Transmute monster, the player would declare that they're either "Transmuting the monster" or "Extra Deck summon-Transmuting the monster.
Another benefit of Transmute monsters is that, while you control a Transmute monster in the Extra Monster Zone, you can summon 1 Extra Deck monster that shares the same Extra Deck monster type as that Transmute monster.
Transmute monsters that aren't Link Monsters can be switched to Defense Position, but cannot be flipped face-down.
Once a Transmute monster is summoned in one state, they must remain in that state whenever they're summoned from the GY or from amongst banished cards (or if they otherwise return to the field).
Transmute Monsters have a scattered triangle effect that, for each side, primarily has the colors of its current side. But will have shades of the color that indicates its other side.