The El Nino Southern Oscillation (ENSO) is a climate pattern that causes major shifts in regional weather patterns across the Pacific, leading to extreme weather events. Australia is particularly vulnerable to ENSO extremes, as exemplified in recent years by the extended drought in the eastern states leading up to massive flooding in 2010-2011. We examine changes in the basic climate state over Australia during two extreme flooding events during La Nina phases, in 1974 and 2010-2011. We employ complementary avenues of analysis, looking at both the synoptics and atmospheric dynamics of the southern hemisphere climate during these events. Synoptically, the circulation over Australia often changes significantly during La Nina phases, with higher SSTs in the western Pacific causing lower pressure over the Indian Ocean, Australia, Indonesia and the western Pacific. These low pressure systems persist over Australia with the aid of blocking high pressure systems, and, coupled with anomalously strong westerly winds bringing down tropical moisture, can lead to intense flooding. Dynamical modes associated with these flooding events are determined using a primitive equation instability model. We find that heavy rainfall is associated with increased growth rates of monsoon disturbances, intraseasonal oscillations, blocking over the Tasman Sea, as well as some changes in the extratropical storm track modes. In particular, we observe unusually explosive and fast-moving equatorial Rossby waves crossing the Pacific just ahead of the January 2011 flooding. Understanding the nature of this climate variability over Australia is a fundamental step in the pursuit of accurate predictions of future ENSO variability, and Australia's future climate and climate extremes.