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The Heat Shock Response (HSR) is a highly conserved genetic system charged with protecting the proteome in a wide range of organisms and species. Experiments since the early 1980s have elucidated key elements in these pathways and revealed a canonical mode of regulation, which relies on a titration feedback. This system has been subject to substantial modeling work, addressing questions about resilience, design and control. The compact core regulatory circuit, as well as its apparent conservation, make this system an ideal ‘hydrogen atom’ model for the regulation of stress response. Here we take a broad view of the models of the HSR, focusing on the different questions asked and the approaches taken. After 20 years of modeling work, we ask what lessons had been learned that would have been hard to discover without mathematical models. We find that while existing models lay strong foundations, many important questions that can benefit from quantitative modeling are still awaiting investigation.