Allotetraploid cotton species are a vital source of spinnable fiber for textiles. The polyploid nature of the cotton genome raises many evolutionary questions as to the relationships between duplicated genomes. We describe the evolution of the cotton genome (SNPs and structural variants) with the greatly improved resolution of 34 deeply re-sequenced genomes. We also explore the evolution of homoeologous regions in the AT- and DT-genomes and especially the phenomenon of conversion between genomes. We did not find any compelling evidence for homoeologous conversion between genomes. These findings are very different from other recent reports of frequent conversion events between genomes. We also identified several distinct regions of the genome that have been introgressed between G. hirsutum and G. barbadense, which presumably resulted from breeding efforts targeting associated beneficial alleles. Finally, the genotypic data resulting from this study provides access to a wealth of diversity sorely needed in the narrow germplasm of cotton cultivars.