A Diviner is a form of Specialist Wizard in Dungeons & Dragons. Their associated school, Divination, is the archetypical "utility mage" school; diviners have no offensive powers inherent to them, but their ability to gather lore and information is unsurpassed, with the ability to read minds, look into the past, see across the planes, and foretell the future.
Ironically, this has made Diviners one of the schools that DMs tend to hate the most, as whilst they don't directly benefit in combat, their spells A: make it almost impossible to run mystery or detective-themed games, and B: support the infamous "Scry 'n' Fry" school of boss-fighting. Diviners are right up there with Enchanters as "the wizarding school of That Guy" - although, at least they don't take forever to do their work as with Conjurers.
Some DMs even outright ban this specialization or school, which isn't unprecedented - the Ravenloft setting quite famously ganks virtually every single Divination spell in some way, from flat out preventing them from working (Detect Evil and its relatives) to just making them not worth the risk (telepathy type spells can result in Sanity damage if you use them on the wrong target).
Scry 'n' Fry
The "Scry 'n' Fry" is a time proven method to both destroy a boss with minimal need to grind through a dungeon, and to make a DM rip their hair out. The process works like this: first you scry the target to find out where they are, then teleport to their location, then 'fry em', and then teleport out. No muss, no fuss.
While most definitely legal, (5e even calls out 'seeing a place with magic' as a valid teleport target), arguably thematic, (its not dissimilar from a space marine drop pod) and unarguably effective (since you're ignoring everything between the bad guy and you, and so expend no resources) it can also make a DM rip their hair out as you make all their efforts at planning the dungeon to be worthless.
As a DM, there are seven options to deal with this. One: house rule it so you can not teleport to a scryed location, but that makes rules lawyers throw a fit since, as mentioned, scry 'n' fry is rule legal. Two: have the bad guy set up anti teleport or scrying magical defenses. Three: roll with it and set up the challenges in other ways. Four: talk to the players. Five: have them be Scry 'n' fryed by something bigger then them.. Six: if the bad guy is important, and paranoid (and in the average high-magic DnD setting, who wouldn't be?) pull a Mario on your players, "The princess is in another castle", and have them be ambushed by the bad guy's guard dog/hydra/dracolich etc... Seven: Inform the players that you are withholding the EXP from the encounters they bypassed, or point out that they're missing out on all the loot therein.
Divination in 3rd Edition work slightly differently from the other schools in that it can't be banned, and only requires a specialist ban one school instead of the normal two. This makes Diviner rather popular since while focusing on divination is questionable, with splat it's not hard to find a divination spell of every level you'd actually want to prepare every day. Even in heavily combat focused games, spells like See Invisibility are often critical. This means you can get the specialist's benefit of an extra spellslot on each level with minimal downside since Evocation is considered relatively painless to ban due to its main role of direct damage being sub-optimal and easily accomplished with other schools.
Diviner is one thing that actually underwent major changes in Pathfinder. Now Diviners have to pick two opposition schools like everyone else that isn't an Elementalist or generalist. Instead, Diviner's limited utility is "balanced" by getting some of the most powerful school abilities. At 1st level a Diviner gets a bonus to initiative while always being able to act in the surprise round. Also at first level is the ability to grant a creature an insight bonus of half wizard level to a wide variety of stuff for one round, which starts weak (standard action for +1), but as a large, versatile bonus of a rare type it means any out-of-combat skill check that requires one round or less becomes a lot easier. At level 8 they also get the ability to tell when someone is scrying on them. This is less useful not because knowing when you're being scryed upon is useless, but because any enemy diviner will quickly learn to start scrying on the low will save fighter instead.
5th Edition's Arcane Tradition
Diviners are still the typical DM's most hated wizardly tradition, and probably the one most likely to get banned at any gaming table. Why? Because the 5e Diviner is a master of screwing with dice rolls and is one of the more complicated of the default Traditions. At level 2, they gain the Portent ability, which lets them roll two D20s after a long rest and take the numbers as notes. They can burn these "saved" rolls to use them as the automatic results whenever they, an ally, or an enemy attempts an attack roll, saving throw, or ability check, although each "saved" roll is only usable once, the Portent can only be used once per turn, and "saved" rolls are lost the next time the Diviner takes a long rest (note that that they can grant or force any being they see one of these rolls). At level 6, they gain Expert Divination; whenever they cast a Divination spell of level 2 or higher, they can regain a spent spell slot, so long as this slot is A: no higher than level 5, and B: is at least one level lower than the spell they cast to gain the refund. Their level 10 ability, The Third Eye, isn't so bad; when the Diviner completes a short or long rest, they can give themselves either Darkvision 60 feet, Ethereal Sight 60 feet, See Invisible 10 feet, or the ability to read any language. Finally, at level 14, their Greater Portent gives them three D20s for Portent instead of only two.
Generally, Expert Divination is just a few extra line items for the player to keep track of, but Portent can be a campaign-wrecker. Why is Portent such a big deal? Because those saved rolls can turn a crucial moment into slapstick comedy. The diviner can point a dominate spell at the BBEG and declare its save to be the three she rolled over cheerios this morning; suddenly the party is playing buddy cop with the doomsday cult leader intended to antagonize the party for years to come. Conversely, good rolls give the diviner a get-out-of-jail-free card against that same BBEG's death spell. Either way it can be an automatic half-henderson or more.
Any plot that can unravel with just one or two key rolls suddenly will, meaning that the DM usually needs to plan a more complex game to engage the party fairly. This in turn plays to the diviner's hands; a diviner is literally a specialist in spells that gain extra information. Put all these pieces together, and you have a character that can put a DM on the defensive... and it's always, always in the hands of a player that does that anyway. If the DM was prepared and expecting this, great, but if the DM (or the other players) were expecting a dungeon-crawling action game this can strain the whole party.
In conclusion: DMs, talk to your players about divination to see if Portent is right for you. (Also, it's like two or three rolls per day, and if your DM is two or three rolls per adventuring day away from having his campaign wrecked, motherfucker needs all the help he can get.)
The Dice Master
A Youtuber by the name of Zee Bashew created a diviner build he bizarrely named "Build Murray" that takes the DM-breakdown-inducing nature of the diviner subclass and cranks it up to Kender/Xaositect levels, and the motherfucker even had the nerve to claim that it's "by no means an optimal build": https://www.youtube.com/watch?v=fSK0AcFqkyU