Simple yield stress fluids

Abstract Recent years have seen a flurry of research on yield stress fluids, approached from different perspectives (physicochemical, rheological and fluid mechanical), considering different length scales and timescales, using a range of tools: experimental, computational and analytical. In this context, it has been common to denigrate the simple models of yield stress fluids for their various acknowledged deficiencies and proffer improved models. Here, we push back, in defence of the century-old simplicity, exploring what is new and useful and what these models have given in the past few decades.