The article analyzes the problems of contemporary professional education. As its instance, we examine the developmental scheme for training professional translators. Optimal ways of organizing the learning process are suggested from the point of view of the competence approach, which is widely recognized for training a modern specialist. The article demonstrates the present-day relevance of the translation profession and the importance of raising expert translators, who possess such a professional quality as a translator's competence. In this article, we analyze different points of view on the concept of "translation competence", as given presently in both national and foreign scientific literature. However, the PACTE-model is specifically highlighted. The problems of developing criteria for the translation quality control are studied, as regards to the translations that future professional translators perform in the process of learning. The article presents various opinions of foreign scientists on the systems of assessment and on the criteria for evaluating the quality of translation services. These systems form the basis for the suggested complex of criteria for the quality control and assessment of translations from Russian, which combines different approaches to assessing translation, and which proved to be productive when used in the process of translators training.