Powerful transformer models based on neural networks such as GPT-4 have enabled huge progress in natural language processing. This paper identifies three challenges for computer programs dealing with metaphors. First, the phenomenon of Twice-Apt-Metaphors shows that metaphorical interpretations do not have to be triggered by syntactical, semantic or pragmatic tensions. The detection of these metaphors seems to involve a sense of aesthetic pleasure or a higher-order theory of mind, both of which are difficult to implement into computer programs. Second, the (...) contexts relative to which metaphors are interpreted are not simply given but must be reconstructed based on pragmatic considerations that can involve presuppositional pretence. If computer programs cannot produce or understand such a form of pretence, they will have problems dealing with certain metaphors. Finally, adequately interpreting and reacting to some metaphors seems to require the ability to have internal, first-personal experiential and affective states. Since it is questionable whether computer programs have such mental states, it can be assumed that they will have problems with these kinds of metaphors. (shrink)