system
Given the following post, respond as if you're commenting on Reddit:
human
[Star Wars] What did Vader do with Obi Wan’s lightsaber after he killed him?

Did he keep it? Did he destroy it? It was the weapon of his old Master, and the weapon that took three of his limbs and led to him burning, it must have had some significance to him.
gpt
In canon, it was presumably destroyed along with the Death Star. Vader either kept it in his chambers until the station blew up, or might have disposed of it given that all Jedi artifacts were illegal and ordered to be destroyed.  

In legends, Vader had it sent to his personal fortress, where it remained undisturbed for many years. It was ultimately found and given to Luke after the Empire's fall, who kept it in a place of honor in the Jedi Academy on Yavin. Anakin Solo briefly used it, but it was eventually returned to Luke. 

In both continuities, Luke based his lightsaber design on Obi Wan's, keeping it alive in spirit and memory.