AbstractHeatwaves in southeastern Australia have characteristic weather patterns that are well understood but are outnumbered by days with similar synoptic‐scale patterns that are not heatwaves. Accordingly, the aim of this study is to identify the key differences between heatwave and non‐heatwave days from 40 years of reanalysis data. A synoptic climatology of seven weather states was constructed by ‐means cluster analysis. Four of these states account for more than 80% of heatwave days across south‐and‐central eastern Australia. Moreover, the spatial maxima in the frequency of the heatwave days are distinct and geographically separated. Heatwave days have a stronger upper anticyclone or ridge that has propagated further equatorward in comparison with non‐heatwave days. The air upstream of the ridge is more humid on heatwave days, whereas downstream of the ridge the air is much drier. These dry anomalies are co‐located with midtropospheric subsidence and the moist anomalies with ascent, and their respective spatial distributions are consistent with regions of adiabatic warming and latent heating identified in recent studies of southeast Australian heatwaves. The corresponding vertical motion on non‐heatwave days is weaker and shifted further poleward. Southeast Queensland heatwave days exhibit increased baroclinicity over the Australian Subtropics and reduced rainfall over Queensland. Further south and west, heatwave days are associated with more amplified Rossby waves and increased rainfall over the Australian Tropics. Anticyclonic Rossby wave breaking is greatly enhanced on heatwave days south of 30°S. For every day in each of these four weather states, the 3‐day‐mean maximum temperature in the region of peak heatwave day frequency is positively correlated with 500 hPa geopotential height anomalies on the equatorward flank of the cluster‐mean upper ridge. These findings underline the importance of equatorward Rossby wave propagation in the dynamics of southeast Australian heatwaves.