Quantum liquid crystal phases are novel states of matter whose symmetries under rotations and translations are between those of a liquid and a crystalline solid. This concept was introduced by Kivelson, Fradkin and Emery about 10 years ago and recently became clear that it plays an important role in the physics, e.g., High Tc superconductors, 2D electron gases.
I this talk, I show that ultracold dipolar Fermi gases develop a particular type of liquid crystal phase, the nematic phase, and hence provide a clean playground for the study of strongly correlated electron systems. Due to the spin-orbit coupling of the dipole-dipole interaction these phases also develop unconventional magnetism. In particular, I will describe two novel phases of matter a) the biaxial nematic phase: which exhibits non-Fermi liquid behavior and b) the ferronematic phase: which resembles states of dense nuclear matter.