1) Background: It has been more than a decade since the concern about addictive use of the Internet and mobile phones was first expressed and its possible inclusion into the lists of mental disorders has been a popular topic of discussion recently, thus it seems to be a fitting moment to investigate the evolution of this issue over time. The aim of the present study was to analyze the evolution of the perception of problematic Internet and smartphone use in young people over the period 2006–2017; 2) Methods: To this end, a questionnaire on Internet use habits and the CERI and CERM questionnaires on negative consequences of Internet and smartphone use were administered to a sample of 792 university students and compared with data from former studies over the period 2006–2017; 3) Results: The perception of problematic Internet and mobile phone use has increased over the last decade, social networks are considered responsible for this increase, and females are the ones perceived to be more affected than males. The degree to which participants agree with the statement “I am addicted to the Internet” can be used as a screening item for problematic use.