Three centuries later, Azog was their leader. When Thror came to reclaim Erebor with Nar, Azog slew Thrór, and this initiated The War of Dwarves and Orcs. The Dwarves hunted down Azog until he was killed by Dain II Ironfoot at the Battle of Azanulbizar. (After Azog's death, his son Bolg would lead an army of Orcs to Erebor, where they lost terribly, and Bolg was killed.) When the Dwarves, led by Thorin turned to Erebor in TA 2989, they came upon bands of orcs who eventually invaded and overtook Erebor, and Thorin was slain. These orcs were large in number and sufficient to keep out any enemies.
The Fellowship of the Ring came upon a large group of Orcs, led by an large orc chieftain, who ambushed and fought them. With these Orcs were others from Mordor, such as Black Uruks spotted by Boromir. Afterwards, the arrival of Durin's Bane caused the Orcs to desist and flee as the Fellowship seeks the exit to Moria in haste. After the Balrog and Gandalf fell into the abyss, Orcs continued their hunt for the Fellowship to Lothlórien, where they were killed by the Elves guarding it.
After the fall of Sauron, these Orcs were driven out of Moria, and the Dwarves reclaimed it.
Portrayal in adaptations
Peter Jackson's The Hobbit Trilogy
In The Hobbit: An Unexpected Journey, legions of these Orcs are shown led by Azog to Moria, in a flashback, where battle ensues. These Orcs fight against the Dwarves led by Thorin Oakenshield, his father Thrain and his grandfather Thrór. Azog manages to slay King Thrór, but loses an arm to Thorin, who then leads his Dwarves against the remaining orcs while Azog is taken by his servants back into Moria.
In extended edition of The Hobbit: The Desolation of Smaug, the Necromancer (who is Sauron in secret) is revealed by Beorn to be in alliance with the Orcs who had infested Moria, as Azog the Defiler is seen paying homage to the dark figure, and his soldiers gather in Dol Guldur where the Necromancer hides.
Peter Jackson's The Fellowship of the Ring
In The Fellowship of the Ring film, after Pippin in Balin's Tomb accidentally knocks a bucket into the dark crevasses of Moria through a well, bands of Orcs are aroused by the noise, and come to attack them. After a skirmish, as the Fellowship run through a great central hall, hundreds of Orcs climb from the ceiling and down tall pillars to surround them. Upon encircling the Fellowship, Durin's Bane (the Balrog) is awoken, and roars, causing the goblins all to flee.