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

Multiferroics and beyond: electric properties of different magnetic textures