The Rise of the Empire
Back in the early days of the Empire, he 501st Legion was made up of Clone Troopers. Theyserved in multiple battles during the Clone Wars, especially near the end. When Order 66 was executed, the 501st - along with Darth Vader - laid siege to the Jedi Temple on Coruscant during "Operation: Knightfall," killing countless Jedi in the slaughter. When the Republic became the Galactic Empire, the 501st remained in service, gaining a reputation as Vader's Fist, engaging in countless battles and conflicts, including the Kamino Uprising, where the cloners rebelled and used their own batch of clones against the Empire. The 501st quickly defeated them, causing Palpatine to consider different options, such as using DNA other than Jango Fett - which was becoming more and more diluted. Unfortunately, as the Rebellion gained strength, the number of victories diminished. Their last, true victory, was had at the Battle of Hoth, where they destroyed the Rebel base. They suffered terrible losses during the Battle of Endor, With the death of Emperor Palpatine, the 501st was disbanded for some time.
After the fall of Emperor Palpatine
While no longer the clones of Jango, the 501st Legion remained a powerful and feared name. They were still active under the Imperial Remnant, where they were made up of the best soldiers the Empire had to offer.
137 years after the Battle of Yavin, Emperor Roan Fel was betrayed from within, and his throne on Coruscant was taken away from him by the One Sith. He retreated to Bastion, where - against the wishes of their commander - the 501st Legion swore their loyalty to the true Emperor, not blind loyalty to the throne. The 501st would fight on the side of the Fel Empire against the One Sith and the Empire that remained loyal to the throne in countless battles during what would be known as the Second Imperial Civil War.
The 501st Legion (named after the real United States 501st Infantry regiment) was initially a fan club for die hard Star Wars fans. However, they became a canon part of the Star Wars universe. Updated information about the Star Wars Universe also names the Stormtroopers who boarded Tantive IV as the 501st Legion.