Overdrive (guitar effect)
The pedal that imitates a valve amp turned up too far — soft clipping, as opposed to fuzz's hard edge.
An overdriven valve stage bends over gradually: play lightly and it stays clean, dig in and it breaks up. An overdrive pedal fakes this with an op-amp and a pair of diodes in its feedback loop that only start conducting once the signal gets strong. The Boss OD-1 of 1977 was among the first, and the Ibanez Tube Screamer TS808 a couple of years later became the template: diodes, a hump in the midrange and a tone knob.
Tube Screamers are often used not for their own distortion but in front of an amp that is already breaking up, to tighten the low end. Bill Finnegan's Klon Centaur of 1994 was built in a few thousand units and now sells second-hand for more than a good amplifier, which has spawned an entire cottage industry of copies known, inevitably, as klones.