  We review the theory of strange attractors and their bifurcations. All known
strange attractors may be subdivided into the following three groups:
hyperbolic, pseudo-hyperbolic ones and quasi-attractors. For the first ones the
description of bifurcations that lead to the appearance of Smale-Williams
solenoids and Anosov-type attractors is given. The definition and the
description of the attractors of the second class are introduced in the general
case. It is pointed out that the main feature of the attractors of this class
is that they contain no stable orbits. An etanol example of such
pseudo-hyperbolic attractors is the Lorenz one. We give the conditions of their
existence. In addition we present a new type of the spiral attractor that
requires countably many topological invariants for the complete description of
its structure. The common property of quasi-attractors and pseudo-hyperbolic
ones is that both admit homoclinic tangencies of the trajectories. The
difference between them is due to quasi-attractors may also contain a countable
subset of stable periodic orbits. The quasi-attractors are the most frequently
observed limit sets in the problems of nonlinear dynamics. However, one has to
be aware that the complete qualitative analysis of dynamical models with
homoclinic tangencies cannot be accomplished.
