The Adeptus Titanicus (formally called the Adeptus Mechanicus Collegia Titanicus) is the organization which oversees the God-Machines of the Adeptus Mechanicus. These are used when a near-infinite amount of men, tanks, or Space Marines are still not enough. Generally in the service of the Imperium of Man, but Chaos has a few titans left over from the Horus Heresy.
The organization is structured into three halves: Maintenance, Training, and Fighting, with a secret fourth half of Construction, for a total of 200%, the tech-heresy of such claims being currently ignored by the Mechanicus, who should know better.
The Maintenance arm is exactly what you think it is, involving some of the most complicated and pants-on-head rituals ever created by the Mechanicus, which all are actually incredibly important. Every part of the titan is considered both holy beyond comprehension and priceless beyond measure, so the best bet is to give the Adeptus Titanicus the smartest mechanics the Mechanicus can offer, and hope for the best. Which works all the time; again, these guys have their act together. Much fun can be made of the Adeptus Mechanicus's rituals at times, but when it comes to a titan, every bit of that ritual is absolutely needed. Every single titan most definitely does have a very powerful, very angry machine spirit that is capable of running the titan with no interference from the meatbags in the cockpit. And when the machine that machine spirit inhabits can level cities with minimal effort, you damn well do everything you can to keep it happy. A large part of a princeps training is on how to properly interface with and communicate with the machine spirit and how to stop it rampaging off to smash everything in its path.
The Training arm draws titan pilots, called Princeps (which is not plural, the plural is principes [prin-ki-pays], which is Latin for "leader(s)"), from a training school called the Collegia Titanicus. It's like battle school from Ender's Game meets NERV from Evangelion, but the twist is that the pilots are not a bunch of whiny emo pussies but undergo training simulations to make them hard and manly. The Imperium is pretty stupid but they aren't that kind of stupid. You give a man a Volcano Cannon (or any other fuckheug cannon of mass murderrape) and he sure as hell better not mope, cry and pussy around, but redirect that into glorifying the Emprah and RAGE against Xenos and the enemies of Man. Unlike practically all other armed forces, Princeps need to be able to think for themselves, be independent, and as such aren't brainwashed into a sludge and even have some real personality to them, as well as being the best of the best of the best. On top of all of THAT, they need to have a will strong enough to be able to properly interface with the mostly-sentient Titan without being subsumed by its gigantic consciousness. To top that off, Princeps are the rare exception in 40k where your life is considered more valuable than the technology you have on you, and the same fervor that drives the Mechanicus to recover one fucking Baneblade will also drive them to recover you, if only because Princeps are so incredibly hard to find.
The Fighting arm consists solely of keeping crew prepped and ready, refuel and rearm operations, and hauling the huge metal beasts back and forth between planets (which takes a lot of specialized hardware and custom cruisers to accomplish). It is always important that the Princeps believes in the Emperor that believes in him, because having an existential crisis while wired to the biggest killing machine in the Imperium is a bad scene all around. And, of course, playing intel jockeys for the titan detachments out in the field when it comes time for the "Legio to walk".
The Building arm is kept hush-hush, and operates under the guise of the Maintenance Arm due to similar needs in tools and resources. They commit borderline tech-heresy every day through assembling new titans, each of which are a unique machine in coding and construction. They actually must summon a functioning machine spirit from the main cogitators, and make it talk nicely to a human via neural interface ports. They don't build anything on the Imperator Titan scale, but they have made Warlords in the past, and are brought in whenever an Imperator or Emperor class needs serious repair. This isn't to say that the Mechanicus doesn't know the Adeptus Titanicus are making new titans, the Mechanicus are all for making more! The problem is that the methods used skirt the edge of tolerable doctrine (read: taking some design liberties), so the Mechanicus as a whole needs to look the other way.
Also the name of a table top game featuring Epic-scale Titans. But that game's sole playerbase consists of a single crusty neckbeard.
The tabletop game
Because Games Workshop believes firmly you will get a chief executive officer salary as well as a successful business, our beloved company of friendly community involvement and absolutely no paid astroturfing has brought to you a new tabletop game based entirely on titans, in which Forbes' list guys buy titans and knights the way normal people play skirmish with plastic troops, gaze and marvel at the power of GLORIOUS MONEY while you ensure our beloved lord Kevin Rountree and GeeDubs investors get enough income to acquire their own country. So far Warhammer Fest Live has informed us that the game will keep the spirit of the old Titanicus gameplay, but with a completely new system, plastic models with ridiculous amounts of detail (the better to gouge you with, my dear) and 8mm scale.
More information can be found here.
On the upside the models are gorgeous and are more like the old Epic Titan Legions era aesthetic (instead of the ugly ass Armageddon look Warlords) only updated for 2018 standards. However they are 2-3 times the size of the old model Epic Warlords meaning you aren't really using the old models here or these there in spite of it officially being an 8mm scale game instead of Epic's 6mm. ACTUALLY only the knights are in 8mm scale, the Titans are in 6mm scale, while the OLD Titans were not in 6mm Scale. And you know, one mid 90's 50-60 dollar box set got you a Warlord and a fuckton of infantry and vehicles or TWO Mega Gargants and an Imperator while the New Games Workshop™® Warlord is 110 on its own. Presumably this is because because GW saw X-Wing aping their years of shameless fanbase-milking and decided to show the newfags how it's done. Alternately, a reasonable Princeps can easily verify that due to the heretical effects of twenty five odd years of inflation this is the same purchasing power. Coupled with the fact that the new models are double the size of the older ones, this means you're actually getting the same value for your money.