The evolution and diversification of many taxa is poorly understood in the arid regions of Australia. In this thesis, I explore the evolutionary responses of arid-occurring dasyurids to Quaternary climate change. I first review the morphology and subspecific status of the endangered northern quoll. I then generate comprehensive molecular sequences to investigate the phylogeography of six small dasyurid species (subfamily Sminthopsinae) occurring in the western arid regions of Australia. Finally, I explore contemporary gene flow in four of these species using a ddRADseq next-generation sequencing approach. The findings will have important implications for the management of arid-occurring dasyurids.