The article presents the challenges faced by safety education in the world of threats posed by the emergence of digital society. As many researchers have already pointed out, the present-day changes associated with technological development affect all areas of life, including ways of making transactions (widespread use of cashless payments) and the acquisition and protection of data. The article defines the notion of digital society, and discusses a few selected threats related thereto. In this context, the authors referred to the need to educate the society in order to prepare it for those new challenges and threats. Special emphasis was placed on the curriculum of primary and secondary schools in Poland.