The development of social productive forces leads to the increasing consumption of fossil fuels. However, the burning of traditional fossil fuels releases huge amounts of carbon emissions into the atmosphere, resulting in drastically increased global surface temperatures, and hence, global warming and abnormal climate change. Biodiesel, which can be produced by (trans)esterification of bio-oils using solid acid catalysts, is recognized as renewable and clean energy, alternative to fossil-derived diesel, and it can meet society's requirements. This review describes the catalytic conversion of bio-derived oils into biodiesel using various sulfonic acid-functionalized heterogeneous catalytic materials that show higher catalytic efficiency and superior recyclability. Besides, various methods of biodiesel preparation and the appropriate design and preparation of robust and efficient catalytic materials for biodiesel production were provided. Finally, the mechanisms of different catalytic esterification and transesterification reactions for biodiesel synthesis, the relevant reaction kinetic models, and techno-economic analysis of biodiesel production were critically discussed in this review. © 2020 Elsevier Ltd.