  This article presents a survey of many nontrivial effects connected with the
coupling of electric and magnetic degrees of freedom in solids -- the field
initiated by I.~E.~Dzyaloshinskii in 1959. I briefly consider the main physics
of ultiferroic materials, and concentrate on different effects "beyond
multiferroics", based on the same physical mechanisms which operate in
multiferroics. In particular they lead to nontrivial electric properties of
different magnetic textures -- such as the appearance of dipoles on magnetic
monopoles in spin ice, dipoles on some domain walls in the usual ferromagnets,
on skyrmions etc. The inverse effect, the appearance of magnetic monopoles on
electric charges in magnetoelectrics, is also discussed. This nontrivial
electric activity of different magnetic textures has manifestations in many
experimental properties of these materials, and it can potentially lead to
novel applications.
