The planetary population synthesis method can help to confront planet formation theory against observations. I will present an overview of recent works and their challenges before focusing on the radius valley in the observed exoplanet distribution. Conventionally, it is explained by the loss of primordial H/He envelopes atop rocky cores. However, this was so far inconsistent with the presence of migrated, water-rich planets which are consistently predicted by planet formation theories. In a recent work, we recover the radius valley at the observed position if we include supercritical steam atmospheres in combination with photoevaporation of mixed H/He and water. The exclusion of the lower-density supercritical phase of water was a shortcoming of previous global models and is identified as a key process.