The current situation in the country has a decisive impact on the field of education, which leads to a more significant introduction and ubiquitous implementation of distance learning not only for teaching students, but also for training of teachers. Distance learning is characterized as an individualized process of acquiring knowledge, skills, abilities and means of human cognitive activity, which basically occurs through indirect interaction of distant participants of the educational process in a specialized environment based on modern psychological, pedagogical, and information and communication technologies. It is shown in the article that many scientific and methodological works analyze positive aspects of distance learning (e.g., mobility, constant access to materials, blended and / or flipped learning, the ability to involve large numbers of participants, efficiency, new teacher role, work in synchronous and / or asynchronous mode, etc.). The presented research revealed the insufficient coverage of existing problems in distance learning, especially distance learning of teachers by modern scientific works (low level of information and communication competence, lack of Internet, outdated equipment, poor self-organization of students, lack of «live» communication, the problem of personalization, copyright violations, etc.). In the paper, the main stages of the history of distance learning beginning from the XVIII century are described. The effectiveness of introducing distance learning of teachers in the postgraduate system of education is substantiated. We explore and analyze pedagogical, methodological and scientific works devoted to the problems of continuous professional education of teachers, professional development of teachers and their qualification improvement. The problems of implementing the distance form of qualification improvement of pedagogical workers in the system of postgraduate pedagogical education are investigated and described in the article.