High-quality and complete reference genome assemblies are fundamental for the application of genomics to biology, disease, and biodiversity conservation. However, such assemblies are only available for a few non-microbial species1–4. To address this issue, the international Genome 10K (G10K) consortium5,6 has worked over a five-year period to evaluate and develop cost-effective methods for assembling the most accurate and complete reference genomes to date. Here we summarize these developments, introduce a set of quality standards, and present lessons learned from sequencing and assembling 16 species representing major vertebrate lineages (mammals, birds, reptiles, amphibians, teleost fishes and cartilaginous fishes). We confirm that long-read sequencing technologies are essential for maximizing genome quality and that unresolved complex repeats and haplotype heterozygosity are major sources of error in assemblies. Our new assemblies identify and correct substantial errors in some of the best historical reference genomes. Adopting these lessons, we have embarked on the Vertebrate Genomes Project (VGP), an effort to generate high-quality, complete reference genomes for all ~70,000 extant vertebrate species and help enable a new era of discovery across the life sciences.