Elysian Drop Troops
Elysian drop troops use rapid deployment tactics to throw troops straight into (or more often, behind) enemy lines. They are famed in battles such as the Taros campaign, the Anphelion project and defense of Betalis. They come from Elysia, a planet about 30 light years away from Armageddon. Elysians are well trained in ship-to-ship boarding actions, ambush and guerrilla warfare as well as fighting in concert with orbital support when attacking enemies.
Hilariously enough, despite being the most competent guardsmen around, in pretty much all canon conflicts they take part in they get dicked over for one reason or another, though it's always due to incompetent command, betrayal of some allies or the fuck-ups of other regiments. The Elysians, on the other-hand, always accomplish their missions and then get killed to a man due to not receiving reinforcements in time. Such is a life of space paratrooper. Maybe they're getting slapped with some kind of bad luck, or there's some heresy going on at Forge World. The actual reason behind this is actually simple: as a Paratroopers, Elysians rely heavily on other regiments' support, which require from those regiments to be fast and creative at dealing with troubles they should inevitably encounter on the way - and if you know anything about the Imperial Guard, you know that that's the exact opposite of what you should expect from 99% of non-Elysian regiments. More so, the Guard is deliberately designed to be flawed like that to ensure other branches of Imperial military may exploit these weaknesses when an army or two turn traitor. Why the fuck did someone decide to make an elite (i.e. expensive to train) force of space paratroopers who most likely are gonna die in their first serious engagement, since Imperial Guard is not designed to effectively work with them at all? Because grimdark, that's why.
Training Elysians usually include throwing kids from the back of moving Valkyries until they learn to use grav chutes, or being shown how to clusterfuck even Orks from behind with only a lasgun. It is a good time to mention that the Guardsmen being trained to do these kinds of things all volunteered to do this, which adds some rather wiry hairs to their massive steel balls. They also often employ Drop Sentinels and the Tauros and Venator vehicles because the Leman Russ Battle Tank is too ponderous for their way of deployment...and heavy armor is for pusses, anyway.
In 6th Edition, with the ability to spam flyers from hell to breakfast, Elysians turned from "interesting tactically-flexible army" to "cheesy cheese of cheesiness," broken far beyond (almost) anything you faced before. Although, like with the Grey Knights, Necrons or Tau, you can create a balanced and interesting army with lots of deep striking guardsman, multi-melta sentinels, and heavy (but not cheesy-heavy) flyer support if you do not want to be a power-gaming douchelord. And by "can" we actually mean "must", unless you want to be beaten to death with old metal dreadnought models by everyone playing with you and/or watching you play.
All in all, the Elysians appear to be an amalgamation of many of the Western world's airborne troops throughout history with a bit of Starship Troopers thrown in for good measure.
We have a tactica for these guys, it's here.