  Correlated electron fluids can exhibit a startling array of complex phases,
among which one of the more surprising is the electron nematic, a
translationally invariant metallic phase with a spontaneously generated spatial
anisotropy. Classical nematics generally occur in liquids of rod-like
molecules; given that electrons are point-like, the initial theoretical
motivation for contemplating electron nematics came from thinking of the
electron fluid as a quantum melted electron crystal, rather than a strongly
interacting descendent of a Fermi gas. That such phases exist in nature was
established by dramatic transport experiments in ultra-clean quantum Hall
systems in 1999 and in Sr3Ru2O7 in a strong magnetic field in 2007.
  In this paper, we briefly review the theoretical considerations governing
nematic order, summarize the quantum Hall and Sr3Ru2O7 experiments that
unambiguously establish the existence of this phase, and survey some of the
current evidence for such a phase in the cuprate and Fe-based high temperature
superconductors.
