It must be acknowledged that the present system of higher education in Russia does not have a system to evaluate the quality of the specialists who are being produced. Three years ago, an order of the education minister approved an appropriate procedure. Seemingly everything is in place: an overall aim, a hierarchical rating system, a structure of criteria, and the method itself. In this article, the author questions whether it is possible to evaluate the quality of specialists being trained in comparison with the following criteria: (1) present world standards; (2) the most pressing needs of the Russian society and economy; and (3) the level of the training in retrospective and perspective terms. The author also explores the components that comprise a good-quality education and proposes a list and a system of criteria for ensuring high-quality training of specialists in Russia.