The observation of significant magnetoresistance anisotropy of a two-dimensional electronic system in very clean GaAs/AlGaAs heterostructure samples in presence of moderately large perpendicular magnetic fields is a striking example of novel anisotropic behavior in the quantum Hall regime. Anisotropy appears to be the strongest at quantum Hall even-denominator filled states for filling factors ν>4 where several Landau levels are occupied. A possible explanation of these findings is due to the existence of charge density waves that are known to cause interesting phase transitions at high Landau levels. An alternative explanation of this phenomenon is to argue that the strongly correlated electronic system has stabilized in an orientationally ordered anisotropic quantum Hall liquid state. Quantum Monte Carlo calculations with a translationally invariant wave function in which rotation symmetry is broken indicate that this might be the case. © 2012 Springer Science+Business Media, LLC.