Due to continuous changes in the society and integration of Russia into the global educational space a transfer to using new educational paradigms has become essential. A competence-based approach is one of them. The paper is devoted to the analysis of the essence of competence-based approach and the historical description of using it in education in Russia and abroad. Description is given of basic stages of introducing competence-based approach to education. The authors present a detailed review of Russian and foreign schools working within the competence-based paradigm. The paper compares Russian and foreign (namely American, English, French, and German) schools. The American school aims at revealing behavioural features of competences and emphasizes personal qualities of the learners. The English school seeks for revealing and improving professional competences on the basis of professional standards. While defining a set of competences, the French school includes both the learners’ behavioural features and their previous knowledge and experience. The German school is also of integrative type and distinguishes professional, personal, and social competences. The Russian educational paradigm involves a fairly large number of competences and their classifications, so the authors describe only some of them (approaches by A.V. Khutorskoy, I.V. Zimnaya, etc.). The authors distinguish between the notions “competence” and “competency”, describe differences in the structure of competences and competency, and present various classifications of competences. The authors conclude that in the competency’s structure all researchers anyway distinguish such components as general (for any area of education) and professional (depending on a certain professional specialization).