Smartphone use by adolescents is increasingly attracting the interest of social scientists, parents, and educational stakeholders (teachers, educators, educational policy makers), generally in a negative context. There are, however, many myths surrounding the issue, resulting from the reproduction of stereotypes about the psychosocial functioning of adolescents in cyberspace, as well as inadequately constructed research tools that measure how new media are used. This text is an attempt to show the phenomenon of problematic Internet use through the prism of screen time measured using real data from smartphones. The research was conducted in first half of 2022 among adolescents aged 13–19 in Bosnia and Herzegovina (N = 1185, mean age = 15.47 with standard deviation = 1.84). The research was implemented using a triangulation of tools such as the Smartphone Addiction Scale (SAS Scale), Software Installed on the Smartphone (SIS Scale), The Bergen Social Media Addiction Scale (BSMAS), and the Screen Time Scale (STS). From the data collected, it was noted that: 1) Screen time correlates weakly with problematic smartphone use and social networking; 2)The average period of smartphone use in the study group is 3 h49 minutes per day, of which 37 min are related to web browsing, while 2 h22 minutes are related to social networking; 3) A quarter of adolescents use a smartphone more than 5.5 h per day, of which more than 2 h15 minutes is screen time related to social media; 4) Approximately half of the respondents use smartphones slightly more than 2 h per day; 5) Girls use smartphones for longer than boys; 6) Place of residence (city or countryside) does not affect screen time; 7) Screen time is related to a medium degree to the type of software installed on the smartphone; 8) There is a need to refine the measurement methodology of screen time and to abandon self-declaration in this area.