Now the Russian healthcare system is rapidly changing. In this period training of future doctors is essential. In the modern conditions when highly qualified medical specialists mastering modern high-tech diagnosis and treatment methods are in demand, the improvement of the quality of training future doctors is one of the important goals of medical higher education institutions. However, the problems of medical higher education institutions are related to the organization of the educational process and limit the full achievement of this goal. Analyzing the results of the sociological survey among practitioners and medical students revealed problems related to the professional and social adaptation of young specialists, as well as the medical personnel's unpreparedness to practice after the graduation. Based on the conducted studies, the article has revealed the limitations that impede the development of the socially important profession -- the doctor, analyzed the level of theoretical and practical training of students, and considered the organization and quality of the educational process for medical students. The authors have formulated recommendations that contribute to improving the modern medical higher education in Russia.