Many of the unsolved problems of physics concern the properties of “fluids” with many strongly interacting degrees of freedom.  Specifically, the physics of “highly correlated electron fluids” underlies the diverse and dramatic macroscopic electronic properties of a large fraction of the currently most intensively studied materials. A gas is easily understood because the interactions between the individual constituents are weak. Conversely, although the interactions between the constituents are strong in a solid, it can largely be characterized by its broken symmetries.  A “simple” liquid is subtle because it is strongly interacting but devoid of broken symmetries. The theory of the correlated electron fluid is difficult for much the same reason. Classical liquid crystals are fluids in which the effects of interactions are manifest in patterns of broken symmetry intermediate between those of the solid and the gas. In the past decade, quantum mechanical (zero temperature) “electronic liquid crystalline phases” have been identified, both in theory and experiment, and considerable progress has been made in theoretically characterizing their properties.  Examples of such phases will be discussed that have been observed in the cuprate and iron-pnictide high temperature superconductors, quantum Hall systems, and the ultraclean transition metal oxide, Sr3Ru2O7.