Project Psyche is a transnational initiative to generate and study chromosome-level reference genomes of all ~11 000 species of Lepidoptera (butterflies and moths) found in Europe. Here, we describe the decentralised network of collection and sequencing hubs that has enabled rapid progress, the standardised protocols for sampling and sequencing, and the collaborative framework for data analysis. With over 1000 species already sequenced, Lepidoptera are at the forefront of biodiversity genomics with the most reference genomes of any eukaryotic order. The completed pan-European catalogue of openly accessible lepidopteran genomes will transform our understanding of evolution and ecology, inform conservation, and foster advances in management of pests and invasive species. We highlight research areas that will benefit from this large-scale genome dataset.