Borrowing language from the field of soft condensed matter, electronic nematic phases in crystalline systems break a discrete rotational symmetry of the crystal lattice without further breaking translational symmetry. In this talk I'll outline methods to measure an associated quantity, the nematic susceptibility, which diverges towards a nematic phase transition. These measurements directly reveal the presence of an electronic nematic phase transition in a family of high temperature superconductors, and an associated quantum phase transition at optimal doping.