The 501st Legion, also referred to as the 501st Battalion and later known as "Vader's Fist," was an elite military division of the Grand Army of the Republic. Consisting of highly-trained clone troopers engineered by Kaminoan cloners, the 501st served under the command of the Jedi Knight Anakin Skywalker throughout the Clone Wars. It was deployed to numerous contested planets across the galaxy during the conflict between the Galactic Republic and the Confederacy of Independent Systems, including Christophsis, Geonosis and Umbara. Command of the legion was temporarily reassigned to Jedi General Pong Krell, whom the 501st mutinied against after learning of his fall to the dark side of the Force. As the war progressed, CT-5555—an Advanced Recon Commando who served in the 501st—discovered a plot to destroy the Jedi Order, but was killed by CC-1010 of the Coruscant Guard before he could prove it.
Although the 501st faithfully served both the Republic and the Jedi, the clone troopers were compelled by their programming to execute Order 66, a secret protocol designed to force the clones into killing their Jedi officers. As such, the 501st marched on the Jedi Temple of Coruscant and, with the aid of Skywalker—now the appointed Sith Lord Darth Vader—proceeded to purge its inhabitants, including Padawans and younglings. Afterward, the 501st gained the nickname "Vader's Fist" and continued to serve as his personal stormtrooper legion under the new regime of the Galactic Empire. Approximately two decades after the proclamation of the New Order, the 501st fought the Rebel Alliance at the Battle of Hoth in 3 ABY during the Galactic Civil War. By then, the Imperial Military had supplanted its clone units with birth-born human recruits.
The 501st Legion was composed of clone troopers that had been engineered as part of an army to serve the Galactic Republic. It was divided into multiple sub-units such as Torrent Company, which served in the first battle of the Clone Wars—the galaxy-wide civil war between the Republic and Separatist Alliance—under the leadership of Clone Captain CT-7567 ("Rex"). Following the Republic victory on Geonosis, the 501st was deployed to the front lines as part of the newly-formed Grand Army of the Republic.
Battle of Kamino
When the Separatists plotted to deal the Republic a crippling blow by destroying the cloning facilities of Kamino, the 501st and 212th rushed to the defense of their homeworld. The Battle of Kamino was a hard-fought victory for the Republic, due in part to the actions of the 501st. In particular, the troopers Echo and Fives were recognized for their service by Captain Rex, as well as CC-2224 ("Cody") of the 212th, and were both promoted to the elite status of ARC trooper in the aftermath of the battle. Afterward, Rex and the new ARC troopers of the 501st were sent with Skywalker and Kenobi to infiltrate the Citadel. Though succeeded in reacquiring the information pertaining to the Nexus Route from General Even Piell and his captain, Wilhuff Tarkin, the group lost Echo, who survived but was presumed dead, in addition to several other casualties.
The 501st Legion utilized the Phase I clone trooper armor during the early period of the Clone Wars, from the first battle on Geonosis until the introduction of the Phase II model by the time of the Battle of Mon Cala. On certain occasions Rex and other members of the 501st made use of jetpacks for aerial transportation and greater mobility.
In general, the 501st maintained the appearance of the standard clone trooper as designed on Kamino. However, Captain Rex became part of a growing trend of clone officers who customized their uniforms with unique color-based designs and supplementary pieces of armor. By the time of the Battle of Christophsis, Rex wore his armor with blue markings, a command pauldron, and a kama. Over time more troopers of the 501st came to customize their own kit, also using blue as a complementary color to the standard white.
As the war continued, Phase II clone trooper armor became widespread within the ranks of the Grand Army, supplanting the Phase I model. When the 501st upgraded their armor, they adopted a common color scheme and markings that identified their unit affiliation. Nevertheless, some clones—such as Rex, the ARC troopers, and even common soldiers—retained their own unique designs that differed from the rest of the 501st.
This has been commander Simple, see you on the battlefield trooper!