Genetic diversity is key to crop improvement. Owing to pervasive genomic structural variation, a single reference genome assembly cannot capture the full complement of sequence diversity of a crop species (known as the 'pan-genome'1). Multiple high-quality sequence assemblies are an indispensable component of a pan-genome infrastructure. Barley (Hordeum vulgare L.) is an important cereal crop with a long history of cultivation that is adapted to a wide range of agro-climatic conditions2. Here we report the construction of chromosome-scale sequence assemblies for the genotypes of 20 varieties of barley-comprising landraces, cultivars and a wild barley-that were selected as representatives of global barley diversity. We catalogued genomic presence/absence variants and explored the use of structural variants for quantitative genetic analysis through whole-genome shotgun sequencing of 300 gene bank accessions. We discovered abundant large inversion polymorphisms and analysed in detail two inversions that are frequently found in current elite barley germplasm; one is probably the product of mutation breeding and the other is tightly linked to a locus that is involved in the expansion of geographical range. This first-generation barley pan-genome makes previously hidden genetic variation accessible to genetic studies and breeding.