Tieflings have been part of Dungeons & Dragons Fifth Edition since the Player's Handbook. This basic version of the Tiefling had several amazing racial abilities in addition to fantastic lore involving their biological connections to the Lower Planes. Tieflings could be born of a relationship between a Fiend and a Humanoid or come about after their parent or grandparent made a deal with an infernal creature.
While originally there was only one option for Tiefling characters, Wizards of the Coast expanded on the race with Mordenkainen's Tome of Foes. The book included nine uniquesubraces for the Tiefling, each based on the bloodlines of different greater Fiends. Each subrace replaces the secondary ability score increase and changes the spells in the Tiefling's innate spellcasting, allowing players to customize their Fiendish character.
Bloodline of Asmodeus
The classic Player's Handbook subrace, Asmodeus Tieflings are perfectly built to be ranged spellcasters. They add a +1 bonus to their Intelligence score, which combined with their default Charisma bonus, makes them a perfect option for Bards, Sorcerers and Wizards. However, the standard Tiefling is most commonly associated with the Warlock class, in part because of their bonus racial spellcasting. Their Infernal Legacy feature gives Asmodeus Tieflings access to Thaumaturgy, an excellent role-playing cantrip, as well as the defensive spell Hellish Rebuke and a utility spell in Darkness.
Bloodline of Baalzebul
Within D&D lore, Baalzebul's domain focuses on corruption and temptation, and players can build on that to develop their character. They get a bonus to their Intelligence score and swap Hellish Rebuke and Darkness for Ray of Sickness and Crown of Madness. Class-wise, Baalzebul Tieflings are well suited to be spellcasters, but they also make great Paladins, as they can take advantage of the racial concentration spells while saving their spell slots for divine smites.
Bloodline of Dispater
Dispater Tieflings are perfectly built to be spies and infiltrators, as their magic allows them to discover secrets through deception and divination. Dispater Tieflings have a bonus to Dexterity, which makes them well suited to be high Charisma Rogues or Bards that specialize in deception. Their racial legacy feature allows them to cast Disguise Self and Detect Thoughts, both of which can be used to gain more information from NPCs or manipulate social situations.
Bloodline of Fierna
Whereas Baalzebul Tieflings focus on physical corruption and pain, Tieflings from the Fierna bloodline focus on emotional and mental manipulation. They gain a Wisdom bonus, which combined with a proficency in Insight, can help them better read those around them. Fierna Tieflings can make amazing Clerics, specifically of the Order and Trickery Domain, as they have a free cantrip in Friends and two of the best enchantment spells in the game: Charm Person and Suggestion.
Bloodline of Glaysa
Masters of illusion, Glaysa Tieflings are descended from Hell's very own prince of crime, so their abilities are designed to complete heists and other criminal endeavors. With an additional Dexterity bonus, they make great Rogues, specifically Arcane Tricksters thanks to their magical capabilities. Instead of Thaumaturgy, members of the Glaysa Bloodline instead learn Minor Illusion, and as they level up they receive Disguise Self and Invisibility, the latter of which helps to set them apart from their Dispater counterparts.
Bloodline of Levistus
While many Tieflings are known for their connections to fire, those descended from Levistus are as cold as ice. Their frozen heritage makes them somewhat sturdier, which helps to explain their Constitution bonus. Levistus Tieflings are the most offensive of the bloodlines, as they are the only subrace to gain an offensive cantrip, Ray of Frost. Combined with Armor of Agathys, this greatly increases their martial capabilities, making them well-suited to be Fighters, Paladins and even Barbarians.
Bloodline of Mammon
Tieflings from Mammon's bloodline have abilities designed to ensure they can take anything they want and keep everything that is theirs. With a bonus to their Intelligence score, Mammon Tieflings can make excellent Artificers and Wizards. Unlike the other subraces, Mammon's inherent spellcasting is focused on manipulating objects rather than people. They learn Mage Hand to help with pickpocketing and lockpicking, along with Tenser's Floating Disk and Arcane Lock, both of which can help to hide a character's most precious possessions.
Bloodline of Mephistopheles
Counterparts of sorts to the Levistus Tieflings, Mephistopheles Tieflings focus on fire instead of ice. However, while the Levistus subrace focuses on offense, Mephistopheles Tieflings gain an Intelligence boost and get a utility cantrip, Mage Hand, to offset their other spellcasting. Mechanically, Mephistopheles Tieflings are better built around ranged fighting and primary spellcasting classes. There Draconic Bloodline Sorcerers and Circle of Wildfire Druids are great options to build on the subrace's fire-based abilities.
Bloodline of Zariel
More than any of the other subrace options, Zariel Tiefilngs are best designed to thrive in melee combat, as they are the only ones that get a bonus to their Strength score. This makes them a great fit for melee-focused classes like Fighter and Barbarian. However, their spellcasting focuses almost completely on Smite Spells, getting Searing Smite at third level and Branding Smite at fifth. The combination of theis STR score increase and smites makes Zariel Tieflings one of the best racial options for Paladins and Hexblade Warlocks.