The new technological order as well as digitalization (digital transformation) of social life are increasingly influencing the regulatory instruments thereof, giving rise to the emergence of technological (digital) branches of law and legislation («digital law» etc.). Until recently, these changes have left almost unaffected the institution of fundamental human and citizen’s rights and freedoms considered as «technologically neutral», i.e. applicable in every kind of environment, including the digital one. Nevertheless, the things here also changing, as evidenced by introduction into the Constitution of Geneva of a new kind of fundamental right entitled - the «right to digital integrity». The article explores and appraises the arguments for and against (pro et contra) the separate consecration of fundamental digital rights and corresponding fundamental digital duties of the State. The research derives from the combination of common scientific and legal exploratory methods together with an interdisciplinary approach (assessment of relevance of digital constitutionalism). The article provides an overview of global constitutional experience of countries of different continents, where the constitutional provisions containing digital rights (DR) have been proposed or are already in force. Taking as a starting point the Swiss legal provisions, the article presents the right to digital integrity and evaluates the positive and negative consequences of its constitutionalisation. Given, the uncertainty of the effects of the abovementioned constitutional innovation the author points out that it is preferable to consecrate the right to digital integrity in federal States initially at the level of federal entities and only later at the national level, as Switzerland did. The author's special contribution to the research of the topic consists in the identification and comparison of conflicting legal arguments supporting and criticizing the specific consecration of digital rights.