There is high confidence that climate change has increased the probability of concurrent temperature-precipitation extremes, changed their spatial-temporal variations, and affected the relationships between drivers of such natural hazards. However, the extent of such changes has been less investigated in Australia. Daily weather data (131 years, 1889-2019) at 700 grid cells (1◦ × 1◦) across Australia was obtained to calculate annual and seasonal mean daily maximum temperature (MMT) and total precipitation (TPR). A nonparametric multivariate copula framework was adopted to estimate the return period of compound hot-dry (CHD) events based on an ‘And’ hazard scenario (hotter than a threshold ‘And’ drier than a threshold). CHD extremes were defined as years with joint return periods of larger than 25 years. Mann-Kendall nonparametric tests was used to analyse trends in MMT and TPR as well as in the frequency of univariate and CHD extremes. A general cooling-wetting trend was observed over 1889-1989. Significant increasing trends were detected over 1990-2019 in the frequency and severity of hot extremes across the country while trends in dry extremes were mostly insignificant (and decreasing). Results showed a significant increase in the association between temperature and precipitation at various temporal scales. The frequency of CHD extremes was mostly stable over 1889-1989, but significantly increased between 1990 and 2019 at 44% of studied grid cells, mostly located in the north, south-east and south-west. Spatial homogeneity (i.e. connectedness) and propagation of extreme events from one grid cell to its neighbouring cells was investigated across Australia. It can be concluded that this connectedness has not significantly changed since 1889.