The paper is devoted to explaining the key cognitive distinctions characteristic to translation process and its teaching. Among them are linguistic interpretation of the input text’s contents, its conceptual adaptation to the accepting culture, etc. To demonstrate them, multiple examples are given to show that translators, particularly not trained enough, often choose for basic translation dominants in the accepting culture those equivalents that are primarily purely linguistic, ignoring conceptual and cultural background of the original and the accepting culture’s notions and forms. Meanwhile, the latter help avoid such translation failures as literal / word by word translation, etc. Special attention in the paper is paid to the translation into the foreign, English, language, its contrastive culture-specific and communicative features as compared to those in the Russian language: to their cognitive dominants in communication and their cross-linguistic asymmetry and in-congruency which generate quite «natural» cross-linguistic interference in Russian-English translation. It is particularly obvious when there are extensive textual nominal ex-pressions, especially terminological, which demonstrate at present an active, extensive and productive usage in English, but present a serious problem in teaching English as a foreign language and translation into it. It is also shown that in Russian their cross-linguistic idiomatic analogues are language specific and show different patterns, but still can be adequately matched with their foreign counter-parts.