The article is dedicated to the necessity of formation and development of digital literacies for the professional, educational and personal purposes. The article also provides a detailed classification of digital literacies and competences. Rapid penetration of information technologies in almost all spheres of our life, including education, and the fact that most ordinary users received unlimited access to the Internet, has led to a rapid rise of the information volume or information explosion and massive changes in the way of communication between people in all spheres and also to forming the information society as one of the leading contemporary social processes. Such changes in socio-economic conditions modified the socio-psychological and psycho-pedagogical portrait of the students, the nature of their participation in educational, professional and social life, as well as the methods of teaching the humanities, computer and natural sciences. The basis of modern educational paradigm are such theoretical concepts as digital literacies, distance learning technologies, information and communication technologies, internet resources, multimedia electronic textbooks, online courses, social networks, Internet resources, individualization and differentiation of learning activities, Personal Learning Network, etc. The importance of improving the educational process through the methodical training of faculty members and tutors, the application of use new technologies in teaching, the formation and development of information and communication competences, digital literacies and knowledge is emphasized.