Heliconius butterflies (Lepidoptera: Nymphalidae) are a group of 48 neotropical species widely studied in evolutionary research. Despite the wealth of genomic data generated in past years, chromosomal level genome assemblies currently exist for only two species, Heliconius melpomene and H. erato, each a representative of one of the two major clades of the genus. Here, we use these reference genomes to improve the contiguity of previously published draft genome assemblies of 16 Heliconius species. Using a reference-assisted scaffolding approach, we place and order the scaffolds of these genomes onto chromosomes, resulting in 95.7-99.9% of their genomes anchored to chromosomes. Genome sizes are somewhat variable among species (270-422 Mb) and in one small group of species (H. hecale, H. elevatus and H. pardalinus) differences in genome size are mainly driven by a few restricted repetitive regions. Genes within these repeat regions show an increase in exon copy number, an absence of internal stop codons, evidence of constraint on non-synonymous changes, and increased expression, all of which suggest that the extra copies are functional. Finally, we conducted a systematic search for inversions and identified five moderately large inversions fixed between the two major Heliconius clades. We infer that one of these inversions was transferred by introgression between the lineages leading to the erato/sara and burneyi/doris clades. These reference-guided assemblies represent a major improvement in Heliconius genomic resources that should aid further genetic and evolutionary studies in this genus.