The Clone Troopers of the 501st Legion were an elite force within the Grand Army of the Republic. They fought in many battles throughout the Clone Wars, serving under Jedi General Anakin Skywalker. They could be identified by their signature blue markings. These troopers were the ones who, when Order 66 was given, helped Darth Vader exterminate the Jedi during their march on the Jedi temple. The 501st's members continued as Stormtroopers, and the legion was placed under the command of Darth Vader, thus renamed 'Vader's Fist." They continued to carry out elite missions for the Empire, such as the boarding of the Tantive IV and the Battle of Hoth, just as they had for the Republic, until the Empire's dissolution.
Perhaps the most notable member of the 501st Legion was Captain Rex, who commanded Torrent Company, a unit within the 501st.