The persistence of the hierarchy problem points to a violation of effective field theory expectations. A compelling possibility is that this results from a physical violation of EFT, which may arise from correlations between UV and IR physics—as is broadly demanded by gravity. I will discuss Noncommutative Field Theory as a toy model of UV/IR mixing, where an emergent infrared scale is generated from ultraviolet dynamics. I’ll explore a variety of such theories to develop a picture of how this feature appears, and to glean lessons to guide the realization of UV/IR mixing in more realistic theories.