The widespread of info-communication technologies in all spheres of human activities gives rise to new threats that in some cases may lead to violation of the constitutional human rights, threaten the stability of the State and public life. Among the most pressing are the ethical problems associated with the digital disparity, violations of personal privacy; ethics conduct on the Internet; compliance of intellectual property rights; opposition to the ideas of violent extremism in the Internet etc. Thus, the problem of improving methodology and content in cyber ethics teaching of university students is very important. The problem of ethics in the field of info-communication technologies is not only the problem of IT specialists. However, professional cyber ethics, as the professional competence and culture of IT specialists is still very urgent. Thus, the urgent problem is the improvement of the methodology and content of future professionals training in the field of cyber ethics. The article focuses on the main problems, challenges and prospects for cyber ethical research, gives the systematic structural approach, and introduces an analysis of questionnaire survey of IT-students on cyber ethics problems. Students' attitude towards cybercrimes in the global network; ethical features of communication in computer networks; ethical aspects of scientific work in the Internet; the problem of Internet addiction and compulsive gambling; the questions of accessibility and censorship of information, attitude to the ethical codes and their implementation in practice (IEEE, ACM, SE, AITPi etc.) were studied. The problems of teaching ICT-ethics in the future IT specialists training at the University are analyzed. Content recommendations and the methods of teaching cyber ethics to IT students are elaborated. The research materials can be used for modernizing current curricula and training programs for university students, for developing and organizing special courses, seminars, elective courses, for conducting scientific schools, scientific conferences.