With the urgent need for the development of sustainable materials and a circular economy, a surge of research regarding biobased materials and associated processing methods has resulted in many experimental biobased foams. Although several biobased foams are already shown to have thermal and mechanical properties competitive with expanded polystyrene, there remains a fundamental knowledge gap leading to limited understanding of the principles that determine performance. This review outlines the progress in this burgeoning field, introducing materials selection and processing, comparing performance, examining efforts in modelling physical properties, and discusses challenges in applying models to real biobased systems. The focus is on low thermal conductivity, which is a critical property for temperature-controlled applications such as packaging for refrigerated/frozen foods, medications, and vaccines as well as building materials. Currently, the trend in the field is moving towards fully biobased and compostable foams, though partially biobased polyurethane foams remain the most consistent performers. To illustrate the foam structure–property relationship, thermal conductivity, cell size, and density data were compiled. Given the complexity of biobased foams, heat transfer models aid in identifying crucial variables. However, data relevant to the insulation capability of biobased foams is not fully reported in many references. To address this issue, we employed a dimensional analysis to fill the gaps, revealing a power law correlation between thermal conductivity and relative density. Our approach is not intended as a robust prediction technique, but rather a simple demonstration of how biobased foams data could be utilized to predict the most promising materials and methods.