An engine is a combination of cards that work well together, but contains too few cards to make a full Deck. If an engine focuses on raising consistency and draw power, it is called a Draw Engine.
Rank 3 engine
These engines use the effect of a specific monster to quickly Xyz Summon Rank 3 monsters such as "Leviair the Sea Dragon", "Wind-Up Zenmaines", "Dante, Traveler of the Burning Abyss", "M-X-Saber Invoker", and "Totem Bird" (if using WIND monsters. There are three notable variants.
"Tour Guide From the Underworld" is used to Summon Level 3 Fiend-Type monster from the Deck. This engine was largely replaced by "Speedroid Terrortop" and "Speedroid Taketomborg", which could achieve the same purpose without wasting a Normal Summon. After "Terrortop's" Limiting, the "Predaplant Ophrys Scorpio" and "Predaplant Darlingtonia Cobra" engine became more prominent; while it uses up the Normal Summon, once per Duel it can also search out a "Fusion" or "Polymerization" Spell Card. Terrortop, however, has remained the standard choice for combo-heavy decks like Gouki, however the banning of M-X-Saber Invoker has once again hurt this variant's viability, as their main Monster of choice to Summon no longer exists in the format.
The Diva Engine is similar to the Tour Guide engine. "Deep Sea Diva" is used to Special Summon another Sea Serpent monster, setting up a Synchro or Xyz Summon. It is more commonly used in "Mermail" Decks, where is possible to search an "Atlantean" monster, specially "Neptabyss, the Atlantean Prince", and provide access to other combos.
The "Machina" engine consists of "Machina Fortress" and "Machina Gearframe". It gives more power to Machine Decks, Including "Gimmick Puppets", "Gadgets", "Geargia" and "Karakuri". "Gear Gigant X" and "Machina Peacekeeper" can be used to search "Gearframe", but the latter is rather not used due to its slow speed.
"Dragon Ruler" engine
When the infamous "Dragon Rulers" were Limited, they were commonly used as engines on Decks of their corresponding Attributes. For example, "Redox, Dragon Ruler of Boulders" could be used to revive "Scrap" or "Karakuri" monsters; "Tidal, Dragon Ruler of Waterfalls" could trigger the effect of "Atlantean" monsters while setting up the Graveyard, and "Tempest, Dragon Ruler of Storms" could fit in any Dragon-oriented Deck, mainly "Dragunity".
"Fairy Tail - Snow" engine
In Decks that rely on filling the Graveyard, specially "Lightsworn" builds, it has been common to use copies of "Fairy Tail - Snow", that can be used as free Xyz/Synchro/Link materials, while banishing useless cards from the Graveyard or cards that trigger their effects upon being banished. Also, since it can be Special Summoned during the opponent's turn, it can also be used as a way to frustrate an opponent's move, acting like a "Book of Moon".
"Brilliant Fusion" engine
This engine consists in Fusion Summoning "Gem-Knight Seraphinite" with "Brilliant Fusion", thinning the Deck with the Fusion Materials while also allowing 1 extra Normal Summon. Depending on the game state, it can provide materials for Link, Synchro, Fusion and/or Xyz Summons. The most popular and consistent way to accomplish this combo is by Normal Summoning "Predaplant Ophrys Scorpio", whose effect is used to Special Summon "Predaplant Darlingtonia Cobra". Then, the effect of "Darlingtonia Cobra" is used to search "Brilliant Fusion", which is finally used to Fusion Summon "Seraphinite". "Performage Trick Clown" is the most common LIGHT Fusion Material used for this Summon, since its effect can be triggered, Special Summoning itself from the Graveyard. This combo results in -4 cards in the Deck, 4 monsters on the field and an additional Normal Summon. The monsters can be used for a variety of Summons, especially of monsters like "Saryuja Skull Dread", "Firewall Dragon", etc. Also, if there was already a Link monster pointing to a Main Monster Zone(s) when "Seraphinite" was Summoned, it is possible to Xyz Summon a Rank 3 monster with the "Predaplant" monsters.