Artificial intelligence (AI) techniques are starting to be used in IVF, in particular for selecting which embryos to transfer to the woman. AI has the potential to process complex data sets, to be better at identifying subtle but important patterns, and to be more objective than humans when evaluating embryos. However, a current review of the literature shows much work is still needed before AI can be ethically implemented for this purpose. No randomized controlled trials (RCTs) have been published, and the efficacy studies which exist demonstrate that algorithms can broadly differentiate well between `good-' and `poor-' quality embryos but not necessarily between embryos of similar quality, which is the actual clinical need. Almost universally, the AI models were opaque (`black-box') in that at least some part of the process was uninterpretable. This gives rise to a number of epistemic and ethical concerns, including problems with trust, the possibility of using algorithms that generalize poorly to different populations, adverse economic implications for IVF clinics, potential misrepresentation of patient values, broader societal implications, a responsibility gap in the case of poor selection choices and introduction of a more paternalistic decision-making process. Use of interpretable models, which are constrained so that a human can easily understand and explain them, could overcome these concerns. The contribution of AI to IVF is potentially significant, but we recommend that AI models used in this field should be interpretable, and rigorously evaluated with RCTs before implementation. We also recommend long-term follow-up of children born after AI for embryo selection, regulatory oversight for implementation, and public availability of data and code to enable research teams to independently reproduce and validate existing models.