  In this review we consider glass states of several disordered systems:
vortices in impure superconductors, amorphous magnets, and nematic liquid
crystals in random porous media. All these systems can be described by the
random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder
destroys long range order in the O(N) model. We demonstrate that at weak
disorder and low temperatures quasi-long range order emerges. In
quasi-long-range-ordered phases the correlation length is infinite and
correlation functions obey power dependencies on the distance. In pure systems
quasi-long range order is possible only in the lower critical dimension and
only in the case of Abelian symmetry. In the presence of disorder this type of
ordering turns out to be more common. It exists in a range of dimensions and is
not prohibited by non-Abelian symmetries.
