The Chitauri are a powerful, technologically-advanced race of extra-terrestrial cyborg-like creatures, and they serve Thanos. They were trapped for eons in the dead space between dimensions. The Chitauri have waited, planning and building for the day their ruler would lead them back into the world of light and life. When Thanos allies himself with the exiled Asgardian Loki Laufeyson, the Chitauri are granted to him as his personal army to conquer Earth and gain the Tesseract.
Once Loki gained the Tesseract from S.H.I.E.L.D., Loki is able to open a portal to the Chitauri's world, thanks to the help of a brainwashed Erik Selvig. The Chitauri immediately starts to wreak havoc and destruction on New York, destroying buildings and attacking civilians in the streets. They quickly established superiority in the city before any significant military force can respond. Soon after their arrival, The Avengers appear, and a major battle begins.
Not expecting such a resistance, the Chitauri are initially overwhelmed, but soon their numbers increase so much from the portal that the superheroes find some difficulties in containing them. Captain America takes command of the Avengers, and thanks to his command, the Avengers' powers are properly used. Hawkeye positions himself on top of a building and takes out several Chitauri flyers, Thor bottlenecks the Chitauri's advance using his lightning powers, the Hulk smashes Leviathans, Iron Man focuses on establishing general air superiority, and Captain America and Black Widow fight off numerous Chitauri infantry’s on the bridge. SWAT teams and patrol officers also fall back and hold Thirty Ninth Street against a Chitauri platoon, stalling the Chitauri advance and allowing civilians to escape.
Eventually, the World Security Council decides to blow up Manhattan with a tactical nuclear weapon in order to contain the Chitauri's invasion at the cost of the civilian’s lives as collateral damage. Despite Fury's attempts to stop it, a rogue S.H.I.E.L.D. jet under orders from the Security Council launches off the carrier and fires a small nuclear missile at the city. Iron Man chooses to bravely intercept the missile and dispose of it. Stark manages to intercept the missile and throw it through the portal, where it blows up Chitauri's fleet, including their Mother Ship, without sacrificing Manhattan to do so. This evidently cuts the link off from the aliens' collective minds and kills all the Chitauri in the immediate vicinity on the other side of the portal.
The Chitauri are a warrior race, a hybrid between organic beings and machines. They're controlled by a Mother Ship which never shows up on the battlefield, instead preferring to stay in the Chitauri's own dimension, far away from the conflict.