Growing demand for broadly accessible mental health care, together with the rapid development of new technologies, trigger discussions about the feasibility of psychotherapeutic interventions based on interactions with Conversational Artificial Intelligence (CAI). Many authors argue that while currently available CAI can be a useful supplement for human-delivered psychotherapy, it is not yet capable of delivering fully fledged psychotherapy on its own. The goal of this paper is to investigate what are the most important obstacles on our way to developing CAI (...) systems capable of delivering psychotherapy in the future. To this end, we formulate and discuss three challenges central to this quest. Firstly, we might not be able to develop effective AI-based psychotherapy unless we deepen our understanding of what makes human-delivered psychotherapy effective. Secondly, assuming that it requires building a therapeutic relationship, it is not clear whether psychotherapy can be delivered by non-human agents. Thirdly, conducting psychotherapy might be a problem too complicated for narrow AI, i.e., AI proficient in dealing with only relatively simple and well-delineated tasks. If this is the case, we should not expect CAI to be capable of delivering fully-fledged psychotherapy until the so-called “general” or “human-like” AI is developed. While we believe that all these challenges can ultimately be overcome, we think that being mindful of them is crucial to ensure well-balanced and steady progress on our path to AI-based psychotherapy. (shrink)