The combination of a nematic or cholesteric liquid crystal and a crosslinked polymer network, either an elastomer or a gel, is a classic example of a hyper-complex fluid system. The orientational interaction between polymer chains of the network and the long range ordering of the nematic phase links the two systems together. Elementary consequences of this linkage include the orienting effects of elastic strains of the gel on the nematic director, and conversely, nematic ordering induced strains of the gel network. However, there are surprising emergent properties of this combination of two complex fluid systems. Certain shear deformation modes of the polymer network lose their elastic restoring force, so that the gel or elastomer behaves somewhat like a fluid, at least up to a point, beyond which an elastic restoring force reappears. These soft modes lead to a number of interesting phenomena, which will be discussed.