  A review is given on the theory of vortex-glass phases in impure type-II
superconductors in an external field. We begin with a brief discussion of the
effects of thermal fluctuations on the spontaneously broken U(1) and
translation symmetries, on the global phase diagram and on the critical
behaviour. Introducing disorder we restrict ourselves to the experimentally
most relevant case of weak uncorrelated randomness which is known to destroy
the long-ranged translational order of the Abrikosov lattice in three
dimensions. Elucidating possible residual glassy ordered phases, we distinguish
betwee positional and phase-coherent vortex glasses. The discussion of elastic
vortex glasses, in two and three dimensions occupy the main part of our review.
In particular, in three dimensions there exists an elastic vortex-glass phase
which still shows quasi-long-range translational order: the `Bragg glass'. It
is shown that this phase is stable with respect to the formation of
dislocations for intermediate fields. Preliminary results suggest that the
Bragg-glass phase may not show phase-coherent vortex-glass order. The latter is
expected to occur in systems with weak disorder only in higher dimensions. We
further demonstrate that the linear resistivity vanishes in the vortex-glass
phase. The vortex-glass transition is studied in detail for a superconducting
film in a parallel field. Finally, we review some recent developments
concerning driven vortex-line lattices moving in a random environment.
