Artificial intelligence (AI) has seen dramatic growth over the past decade, evolving from a niche super specialty computer application into a powerful tool which has revolutionized many areas of our professional and daily lives, and the potential of which seems to be still largely untapped. The field of medicine and medical imaging, as one of its various specialties, has gained considerable benefit from AI, including improved diagnostic accuracy and the possibility of predicting individual patient outcomes and options of more personalized treatment. It should be noted that this process can actively support the ongoing development of advanced, highly specific treatment strategies (e.g., target therapies for cancer patients) while enabling faster workflow and more efficient use of healthcare resources. The potential advantages of AI over conventional methods have made it attractive for physicians and other healthcare stakeholders, raising much interest in both the research and the industry communities. However, the fast development of AI has unveiled its potential for disrupting the work of healthcare professionals, spawning concerns among radiologists that, in the future, AI may outperform them, thus damaging their reputations or putting their jobs at risk. Furthermore, this development has raised relevant psychological, ethical, and medico-legal issues which need to be addressed for AI to be considered fully capable of patient management. The aim of this review is to provide a brief, hopefully exhaustive, overview of the state of the art of AI systems regarding medical imaging, with a special focus on how AI and the entire healthcare environment should be prepared to accomplish the goal of a more advanced human-centered world.