Dark energy is a cosmic field with negative pressure. The possibility that this pressure may vary with direction is motivated by several recent theoretical considerations. In this talk we show that such models are not only cosmologically viable but that they could explain some of the observed anomalies in the cosmic microwave background (CMB). In addition to CMB, the anisotropy can be constrained through its effects on the large-scale structure. New observables for dark energy are introduced by the cosmic parallax and the anisotropies in the various cosmic distance-redshift relations.