  The article reviews recent developments on magnetic properties of
superconductors with anisotropic Cooper pairing. In particular, we show how the
concept of broken symmetries is applied to the investigation of the mixed state
in superconductors with a multicomponent order parameter. Starting from the
phenomenological description in the framework of the generalized
Ginzburg-Landau theory, we discuss different types of quantized vortices
appearing at $H_{c1}$ in states with and without time-reversal breaking.
General classification of superconducting phase transitions in a uniform
magnetic field at $H_{c2}$ is constructed. Vortex lattices of different forms
are found in the vicinity of the upper critical field. Symmetry arguments are
used to classify phase transitions inside the mixed state. Special attention is
given to results which can be obtained analytically. Also special emphasis is
put on the open questions of the theory.
