Chainsword
The Chainsword is a fuckawesome melee weapon, heavily used by Imperial forces, although the Eldar, Orks, and Chaos Space Marines also field it. Apparently in the 41st Millennium chainsaws have been repurposed for the use in hacking down people/aliens/things instead of hacking down trees. As its name mentions, the chainsword is a twin-bladed weapon with a rotating chainsaw blade in-between, that's powered by a motor mounted on the hilt and activated with a trigger on the grip.
Although the chainsword is issued to virtually all Imperium forces, it is most famous with the Spehss mahreens who widely use the chainsword as the primary weapon of their assault troops and veteran soldiers. The only fucking problem is that it doesn't have special rules, beside Eviscerators and shit like that. GW Is basically saying getting hit with a chain axe, or chain sword has the same effect as a combat knife.
Variants
The Chainsword also has several variants that hav been developed by both the Imperium of Man and Xenos. Here are some examples:
Eviscerator
An oversized chainsword used by the Ecclesiarchy's priests or by the Sister Repentia of the Sisters of Battle (as well as Chapter Master Gabriel 'IN THE BALLS' Seth). The Eviscerator is twice the size of a regular chainsword and so heavy that a normal soldier will need to carry it using both hands. The Eviscerator might also incorporate an exterminator, a portable flame unit that will not only help it breach armor, but scare a normal man shitless upon seeing a man swinging the fucking thing. The Eviscerator is also extra effective against armored units.
Scorpion Chainsword
An Eldar variant of the Chainsword fielded by the Striking Scorpions. It's like the Imperial Chainsword but incorporates advanced equipment that increases the wielder's strength and a sleeker, less bulky design.
Exarchs can use two variations of the Scorpion Chainsword: the Biting Blade (a massive two-handed weapon whose effectiveness increases as a target is hit), and the Chainsabres (two one-handed chain weapons that can land a truly staggering amount of blows on a target.
Chainaxe
Yes, Warhammer has chainsaw axes, as insane it sounds. The custom weapon of Khornate champions, the Chainaxe was ironically a fairly common weapon among Imperial troops pre-heresy. It's basically a huge axe with a powerful chainsaw as a blade. The sheer weight of the axe and the fact that most Khorne Chaos Marine champions are super strong and borderline psychopaths completely fucking nuts: these are capable of ripping through most infantry armors. They see a lot of use with non-Khornate Chaos Marines as well, due to the greater damage they inflict. Among Imperial forces, you are most likely to see a chain-axe in the hands of a Space Wolf or Raven Guardsman - the former due to the fact that they just don't give a flying fuck that it might associate them with Chaos, and the latter due to the fact that they mostly have older equipment due to infrequent resupplies.
Chainglaive
The Chainglave is an evolution of the Chainaxe, giving it a longer blade and haft allowing for wide, sweeping strikes. It's used extensively by Vanguard Marines and Chaos close-combat specialists. An ancient design by modern standards, it's by no means common, and sees use primarily with the traitor legions due to this.
Chainbrush
The weapon of choice of the Adeptus Orthodontus. It's based as a spear with the blade being a consecrated toothbrush/chainsaw blade. It purifies even the most revolting of mouths from the forces of oral diseases.
Chainfist
Intended for Terminators involved in boarding actions, the Chainfist is a Power Fist that incorporates a powerful chainsaw blade for the purposes of slicing through armored bulkheads. The weapon is commonly used by Terminators as a CQC weapon, and to rip the armor off Space Hulks during boarding actions. Because it can knife through thick metal with little trouble, it's often used for ripping open enemy vehicles and bunkers.
Choppa
The choppa is the ork version of the chainsword. The weapon is a handheld chainsaw (though it sometimes takes the form of a sword or axe) used for almost anything, really you name it anything ranging from a weapon to a household tool. While choppas or regular Ork boyz rarely have the actual chainsaw blade on their weapon, richer Orks like the Warboss or a Nob might have it on theirs to make it killy and flash. Many are simply war trophies picked up from Space and Chaos Marines.