The genus Amaranthus consists of 50 to 70 species and harbors several cultivated and weedy species of great economic importance. A small number of suitable traits, phenotypic plasticity, gene flow and hybridization made it difficult to establish the taxonomy and phylogeny of the whole genus despite various studies using molecular markers. We inferred the phylogeny of the Amaranthus genus using genotyping by sequencing (GBS) of 94 genebank accessions representing 35 Amaranthus species and measured their genome sizes. SNPs were called by de novo and reference-based methods, for which we used the distant sugarbeet Beta vulgaris and the closely related Amaranthus hypochondriacus as references. SNP counts and proportions of missing data differed between methods, but the resulting phylogenetic trees were highly similar. A distance-based neighbor joing tree of individual accessions and a species tree calculated with the multispecies coalescent supported a previous taxonomic classification into three subgenera although the subgenus A. Acnida consists of two highly differentiated clades. The analysis of the Hybridus complex within the A. Amaranthus subgenus revealed insights on the history of cultivated grain amaranths. The complex includes the three cultivated grain amaranths and their wild relatives and was well separated from other species in the subgenus. Wild and cultivated amaranth accessions did not differentiate according to the species assignment but clustered by their geographic origin from South and Central America. Different geographically separated populations of Amaranthus hybridus appear to be the common ancestors of the three cultivated grain species and A. quitensis might be additionally be involved in the evolution of South American grain amaranth (A. caudatus). We also measured genome sizes of the species and observed little variation with the exception of two lineages that showed evidence for a recent polyploidization. With the exception of two lineages, genome sizes are quite similar and indicate that polyploidization did not play a major role in the history of the genus.