Fusion

Fusion, or Union (合体, gattai), is the system in which two or more demons are combined together to create a new demon. A demon created via this system will inherit certain traits and abilities from the "ingredient" demons that were used to create it. The exact nature of this inheritance varies by the types of demons used in the fusion, by the type of demon being created by the fusion, by the phase of the moon (or its equivalent), and by other factors that vary by game.

The general rule for the most basic two-demon fusion is: race A demon fuses with race B demon results in race C demon with slightly higher level of the average of the ingredient demons. But there are many exception to this rule.

Some demons cannot be recruited or captured normally, and must instead be created via special fusion. Some of these demons can only be fused once certain prerequisites have been met; for example, some bosses can only be fused once they have been defeated.

In several games, demons can also be fused into weapons (usually swords), giving that gear new abilities based on the abilities of the demon used in the fusion.

Clarification
In Japanese titles, literal Fusion (フージョン) when used, does not refer to traditional Devil Union. The word "Union" is more often used by Atlus Co., Ltd. when unambiguously rendering this concept in English.

Megami Tensei series
In Megami Tensei games, gattai (合体, "union"), called fusion here, is possible at a Jakyou no Yakata (邪教の館, "mansion of the infernal master[s]")

Shin Megami Tensei series
In the main Shin Megami Tensei series, fusions are made at the Cathedral of Shadows (Jakyou Manor). The first three installments of this series include three-demon fusion which gives player access to create more powerful demon than in two-demon fusion but with more complicated rules. Shin Megami Tensei: Nocturne has the unique sacrificial fusion mechanic, which is only carried out in a Full Kagutsuchi phase.

Last Bible series
In the English-language localization of Last Bible (localized under the title Revelations: The Demon Slayer), fusion is referred to as Combination. Fusion is performed at shrines rather than the Cathedral of Shadows.

Devil Summoner Series
In the Devil Summoner series, demons are fused by Victor at the Gouma-Den. In the Raidou Kuzunoha sub-series, demons can only be used in normal (non-sacrifice) fusion if they have maximum loyalty.

Persona Series
In the Persona series, Personae can be fused in Igor's Velvet Room in the same manner that demons are fused in most other games.

DemiKids
All demons fused with the respective partner demon act as Mitamas. Fusing Shiny demons with the same demon it's a shiny version of will also result in the Shiny demon increasing two stats. Fusing multiple versions of the same regular demon together will result in a increase of HP and MP until they are fused a certain number of times, after which they will fuse to become a demon of a higher rank.

Relic Fusion is a special fusion where you take fossils that can be bought in the game and fuse three of them together. This can result in either a zombie version of certain demons or a regular demon being born. Resurrecting Zombie fusion will result in a zombie demon being brought back to life after its soul is fused with it.

Shin Megami Tensei: Strange Journey
Fusion in this game is handled through the specialized Demon Fusion Program, which alongside the Demon Summoning Program is sent to the Schwarzwelt crew through a hacked AI, Verne, the brother AI to the crew's Arthur, from an unknown source by The Three Wise Men.

Jack's Squad also attempted to perfect Demon Fusion protocols without the intervention of the Three Wise Men, but their techniques were terribly flawed at best; this, coupled with their lack of the Demon Summoning Program and Demon Fusion Program meant they were forced to enslave demons rather than convince them to join them by negotiation, and that most of their higher level demons were mostly abominations such as Slimes, Pellaidhs, Pisacas, Ghouls, or Legions.

This would have severe implications for the story as their attempts to fuse demons and humans and abusing demon prisoners came into the fore.

Aside from that, the game also boasts a Special Fusion technique, which allows for the fusion of more than two demons into a single, more powerful one. However, the ingredients for these fusions are fixed and cannot be exchanged by similar substitutes.

Devil Survivor Series
In all games of the series, demon fusion takes place using the Cathedral of Shadows Program (often termed cath.exe) that is introduced with the Demon Summoning Program. In all games to date, only two demons can be used for fusion. Unlike previous games in the entire Shin Megami Tensei series, the player has control over what skills the resultant demon inherits from its fusion components, and can even search what demons are required to produce the desired result. If the fusion components have increased stats (either from levelling up or prior fusions), the resultant demon can also inherit a portion of those stats (albeit distributed somewhat randomly).