The article is devoted to the current problems of changing language norms under the influence of information and communication technologies. Some theoretical provisions on the specifics of linguistic norms in functional (i.e. norms widely used in speech) and codification aspects (i.e. norms fixed in normative legal acts, dictionaries, reference books, textbooks and grammars) are considered. Some distinctive parameters of the linguistic norms are described as a heterogeneous category characterized, on the one hand, by conservatism, stability, commitment, exemplary, directive and other constant features, on the other hand, by dynamism, instability and variability. The last ones often lead to linguistic deviations. Transformations of linguistic norms in the Internet give an impetus to the emergence of new concepts and the formation of new terms such as “Russian digital literary language” (A.V. Kozulyaev), “criticism of the Internet language” (K. Durscheid), “grammar nazi” and others. The article contains some examples of violations and changes of the norms of the Russian and German languages in the electronic communication. Two areas of criticism of the Internet language are considered: writing (or written texts) and communicative behavior in the Web. Deviations of linguistic norms at different levels (graphic, spelling, lexical, syntactic) in Russian-language online communication are revealed. There are also some prospects for research in this area.