In condensed matter physics there is a long history of the study of structural phase transitions. They were the prime examples used by Landau to develop his theory of phase transitions. In recent years, it has been realized that ferroelastic instabilities can be driven by an ordering of correlated electrons that are also responsible for electrical conduction and/or superconductivity. In this talk I will outline a new technique based on elastoresistance measurements, which directly measures the fluctuations of this underlying electronic order. In particular, I will show measurements that reveal the prevalence of electronic nematic fluctuations in a family of high temperature superconductors. These results suggest that there is a quantum phase transition near the composition with optimal superconducting transition temperature.