Drought is one of the most complex hydroclimatic extremes, with enormous effects on the environment, economy, and society. In many locations, climate change is expected to increase the severity and frequency of droughts. However, most climate change impacts to date focus on relatively short-duration droughts (e.g., 12 months) and do not consider the evolution of droughts in terms of time or space. This means that evaluation of climate models and projections based on those same climate models are limited to point-by-point analyses with no information on drought evolution and decay and the future changes in these attributes. The multi-scale nature of droughts which can last over multiple years is also not considered in many climate change impact assessments which use fixed temporal windows for analysis. This thesis proposes new methods to address these issues and applies the new methods to analyse future drought across Australia with a specific focus on the spatial and temporal evolution of drought historically and in the future in the Murray Darling Basin (MDB). The main methodological contribution of the thesis is a new multi-time scale drought index termed the Residual Mass Severity Index (RMSI). The RMSI improves on the existing drought indices because it does not require a temporal window to be specified to characterize extreme deficit periods and these periods can be automatically identified. The RMSI is then used to evaluate the performance of general circulation models (GCMs) in characterizing historical drought. There is a reasonable consistency in GCMs in terms of representing drought frequency but only a few GCMs exhibited acceptable skill in capturing drought recovery and peak magnitude of drought. Spatiotemporal drought evolution was then characterized in the MDB. The areas worst affected by drought tend to experience faster build-up and slower recession than the basin as a whole. Finally, spatiotemporal changes in drought characteristics in MDB represented by GCMs in the current and future climate were assessed. Overall, an increase in drought duration, severity, and time to recede are projected for the future.