The paper develops applied and theoretical results obtained by the author in a long-term, corpus-based research on the cross-linguistic scientific communication and on its most distinctive problem — translating modern scientific texts mainly on digital information processing from English into Russian (and vice versa). These texts are characterized primarily by the growing number of multi-word language-specific new terms. In this respect special attention is paid in the paper to modern authentic «digital» neologisms-clusters in English: to their cross-linguistic idiomatic character, their language-specific types and patterns, to their systematization as well as to their communicative and cognitive distinctions. The paper introduces their equivalent terminological counterparts in Russian and the way they are to be translated into Russian. Some important generalizations and proposals are also introduced concerning new trends in the formation of language-specific «digital» terminological clusters in English and the way they can be rendered into Russian. The paper concludes with outlining some further perspectives in studying cross-linguistic scientific communication, its new terminology and developing its cross-linguistic translation, particularly by digital resources.