Garrosh Hellscream is an orc and part of the Mag'har (uncorrupted orcs), hence his brown skin rather then the usual green. Garrosh's first appearance was in The Burning Crusade expansion pack where he was introduced as the son of Grom Hellscream, an old friend to Thrall (Leader of the Horde). Originally all he knew of his father were stories of him being the first to drink the demon blood and fall under the bloodcurse (a constant state of aggression) which corrupted most orcs. When the Dark Portal was opened, Thrall meets Garrosh and tells him his father went on to save all of the orcs from the bloodcurse. Towards the end of the events of The Burning Crusade, Thrall took Garrosh with him back to Orgrimmar. In the Wrath of the Lich King expansion, Garrosh led horde forces in Northrend under the supervision of Saurfang. During the events of the Cataclysm expansion Thrall chooses Garrosh to replace him as Warchief of the Horde, a controversial decision which has led to a lot of internal friction within the Horde. Garrosh's leadership also brought an increase in aggression against the Alliance. Over the course of the Mists of Pandaria expansion, Garrosh has sought various ways to increase his power using dangerous dark artifects. The internal conflict his leadership caused within the Horde has escalated to a full out rebellion lead by Vol'jin.
The Burning Crusade
Garrosh starts off sullen and depressed, fearing that once he becomes the leader of the Mag'har he will make the same mistakes his father did and doom his people. This is due to the Mag'har (and thus him) only knowing Grom as the leader of the Warsong Clan who was the first orc to drink the demon blood that cursed almost every orc. However once the Dark Portal is opened Thrall arrives and tells Garrosh how, along side him, Grom killed the demon that cursed them and freed all the orcs from their bloodcurse. Thrall being a loyal friend of Grom therefore paints him as a hero of the orcs. Garrosh later agrees to return to Orgrimmer with Thrall.
Wrath of the Lich King
In Orgrimmer, at a meeting of many leaders of the Horde (including the faction leaders), Garrosh challenged Thrall for leadership of the Horde, believing, contrary to Thrall, that they should aggressively invade Northrend and claim it for the Horde. However their battle is interrupted by an attack by the Scourge, which they both must help defend. Thrall later sends Garrosh to command some of the Horde forces in Northrend under the guidance of Horde veteran, Saurfang. Garrosh regularly accompanies Thrall to meetings such as one in Dalaran, about the danger Ulduar poses. At these meetings he regularly shows a hatred for the Alliance and outward aggression towards them, even though they are supposed to be on neutral territory.
When Garrosh returns from Northrend, Thrall reveals that he shall leave the position of Warchief of the Horde to dedicate himself to becoming a powerful shaman in order to try and mend the world in the wake of the cataclysm. Before Thrall leaves however, he chooses Garrosh as his successor. This causes drastic changes in Horde politics and in Orgrimmar. Garrosh is challenged to an honour duel by Cairne Bloodhoof, Chieftain of the Tauren, but Garrosh's axe is secretly poisoned by one of Cairne's enemies, leading him to easily win and kill the Tauren leader, who was succeeded by his son Baine. Garrosh soon also falls out with Vol'jin, leader of the Darkspear Trolls, who promises Garrosh that he will fire the arrow that pierces his heart. There is also some friction between Garrosh and Sylvanas Windrunner, leader of the Forsaken Undead, when the Banshee Queen announces that with the help of the Val'kyr, she can create new Forsaken and prevent them from slowly dying out. Garrosh has also enacted many aggressive pushes for more territory using Horde forces.
Mists of Pandaria
Garrosh ordered the destruction of Theramore (Run by the normally peaceful human mage, Jaina Proudmoore) using a mana bomb. The attack horrifies not only Jaina and the Alliance, but also much of Garrosh's own horde, particularly Vol'Jin and Baine who already think exceptionally poorly of him. Once Pandaria was discovered, Garrosh arrived with much of the Horde fleet, setting up a small base in Karasang Wilds and immediately contending with the Alliance for control of the area. While in Pandaria, Garrosh actively sought powerful artifacts to enhance his power further and strengthen the Horde. He has also sent the Blood Elves, lead by Lor'themar Theron, to the Isle of Thunder. This decision is mostly due to Garrosh's view that the Blood Elves have failed to be useful to the Horde, having been almost completely absent from the campaign he oversaw in Northrend and many of the varying skirmishes against the Alliance. Garrosh's thirst for war has united his enemies against him - not just the Alliance, but the Horde as well. The resentment and hostility within the Horde towards Garrosh's leadership has exploded into all out rebellion as Garrosh brands all Darkspear Trolls traitors to the True Horde. The rebellion is lead by Vol'jin, who is aided by Chen Stormstout, Baine and supported by all the other Horde leaders. Voljin's rebellion attacked Orgrimmer itself and even had Alliance support and aid as the two form an uneasy treaty. All with the goal of deposing Garrosh and returning order to the Horde.