Since generative AI hit the mainstream in 2022, litigation about generative AI and copyright infringement has been extensive, but there have been very few substantive judgments, and the vast majority of litigation is in the US, where summary judgments on the 'fair use' defence have not yet addressed liability for training on crawled datasets. No final US decisions on liability have been reached, even at first instance, though several first instance decisions on liability have been reached elsewhere. Appeals to the highest courts seem inevitable, and without further legislative intervention, certainty will take several years. The main focus of litigation has been the AI training process, with some cases also considering whether pre-trained models contain infringing copies or whether a model itself constitutes an infringing copy, and whether outputs infringe copyright. Most courts have considered training, the status of the trained model, and outputs as separate acts, though some have treated them as a unitary process. The status of infringement by users when inputting copyright works as prompts or using RAG raises further questions, but courts have yet to address these issues. It is clear that many LLMs and diffusion models were trained using copyrighted content without a licence, and the big open question is whether such unlicensed training is permitted under copyright law.