The radii of hot Saturns are among the most poorly understood for any type of planet. Their mass-flux-radius relationship exhibits properties which are entirely unique to them. They transition from a strong flux-radius correlation at high masses to no correlation at low masses. Some are clearly inflated and H/He-dominated, while others are almost devoid of H/He. Worse, simple structure modelling suggests that at least some lower mass inflated planets should be larger than is actually observed. To better understand these objects, we have applied Bayesian statistical retrievals and interior structure evolution modelling to identify the compositions and anomalous heating that can reproduce the radii of observed hot Saturns. We discuss the implications for their formation and subsequent evolution — in particular, we argue that for especially hot planets, significant mass loss occurs at masses much greater than has been previously thought.