This text intends to provide an introduction on how the challenges posed by Artificial Intelligence systems (AI systems) to the theory of criminal responsibility have been considered or solved in the Portuguese legal system and academic debate. Firstly, the main aspects are considered from a general point of view, in terms of law and regulation. We describe the existing legal framework regarding AI systems in Portugal and identify a dominant sectorial approach. Secondly, we focus on criminal law and criminal responsibility in three different perspectives: existing criminal offences (cyberthreats, cybercrimes and crimes committed by, through or against an AI system); main challenges for the traditional criminal law categories of the general part of the Portuguese criminal code (legality principle, corporate criminal liability, causality, state of mind, perpetration, Garantenstellung, alternatives to criminalization); and, finally, a reference to the Portuguese academic debate concerning these challenging issues.