The Tasmanian devil (Sarcophilus harrisii) was widespread in Australia during the Late Pleistocene but is now endemic to the island of Tasmania. Low genetic diversity combined with the spread of devil facial tumour disease have raised concerns for the species' long-term survival. Here, we investigate the origin of low genetic diversity by inferring the species' demographic history using temporal sampling with summary statistics, full-likelihood and approximate Bayesian computation methods. Our results show extensive population declines across Tasmania correlating with environmental changes around the last glacial maximum and following unstable climate related to increased 'El Niño-Southern Oscillation' activity.