Many guitar gear reviewers (one example) claim that tube screamer was designed to run into dirty amp. While it's definitely common application for all mid humped overdrive pedals (especially ones with clean signal passing through) I've never found evidence of that being part of pedal design. Is this a myth?
Since the most iconic Tube Screamer sounds I can think of (e.g., Stevie Ray Vaughan and Trey Anastasio) have been created using very clean amp sounds, and distortion/overdrive pedals were invented to be used instead of overdriving an amp (back in the days when amps didn't generally have drive circuits and the only way to overdrive them was to turn them way up), it seems almost certain that it was not originally meant to run into a distorted amp.
This article suggests the Tube Screamer (and the Boss OD-1) were meant to give guitarists good overdrive sounds when using solid state amps, which were generally run clean and sounded pretty terrible if distorted: