Angel's showrunners history
Created by Joss Whedon and David Greenwalt,for the first 3 seasons the showrunner was only David Greenwalt (while Joss Whedon was a very active executive-producer,writing and directing several episodes). Then,in season 4,David Greenwalt created a new show,so he left his role as showrunner,and David Simkins was hired as showrunner instead. But,as he was a new writer and not someone who was in the writing staff and promoted,he probably had issues in fitting into Angel's writing style,so he left after a few weeks for creative differences. So Jeffrey Bell,who was already in the writers staff,was promoted to showrunner for season 4. And during that season,Joss Whedon was less active as executive producer because he was already too busy with the final season of Buffy,and the first season of Firefly,and he was also writing some scripts to realize a Batman and a Wonder Woman movies for DC Comics,movies that never happened.
In season 5,instead,as Joss Whedon was finally free from Buffy and Firefly,he basically acted as showrunner for season 5 together with Jeffrey Bell. So,quick recap:
Seasons 1-3: David Greenwalt
Season 4: David Simkins (then replaced),Jeffrey Bell
Season 5: Joss Whedon and Jeffrey Bell