Polyploidy plays an important role in evolution because it can lead to increased genetic complexity and speciation. It also provides an extra copy buffer and increases genetic novelty. While both common and well-studied in plants, polyploidy is rare in animals, and most polyploid animals reproduce asexually. Amphibians represent a dramatic vertebrate exception, with multiple independent sexually reproducing polyploid lineages, but very few cases have been studied in any detail. The Australian burrowing frog genus Neobatrachus is comprised of six diploid and three polyploid species and offers a powerful model animal polyploid system. We generated exome-capture sequence data from 87 individuals representing all nine species of Neobatrachus to investigate species-level relationships, the origin of polyploid species, and the population genomic effects of polyploidy on genus-wide demography. We resolve the phylogenetic relationships among Neobatrachus species and provide further support that the three polyploid species have independent origins. We document higher genetic diversity in tetraploids, resulting from widespread gene flow specifically between the tetraploids, asymmetric inter-ploidy gene flow directed from sympatric diploids to tetraploids, and current isolation of diploid species from each other. We also constructed models of ecologically suitable areas for each species to investigate the impact of climate variation on frogs with differing ploidy levels. These models suggest substantial change in suitable areas compared to past climate, which in turn corresponds to population genomic estimates of demographic histories. We propose that Neobatrachus diploids may be suffering the early genomic impacts of climate-induced habitat loss, while tetraploids appear to be avoiding this fate, possibly due to widespread gene flow into tetraploid lineages specifically. Finally, we demonstrate that Neobatrachus is an attractive model to study the effects of ploidy on evolution of adaptation in animals.