Abstract Bottlenecks on the development of biodiesel production could be eliminated using direct transesterification (DT). This review presents a comprehensive overview for DT from oleaginous seed crops (edible and non-edible), microalgal and fungal/yeast biomass. Effects of key operational parameters, affecting the yield of biodiesel, such as feedstock, feedstock processing technologies, feedstock water content, catalyst choice, temperature, co-solvent and reaction time are summarised and critically assessed. 15% and 68% of published data showed high fatty acid (FA) yields and FA to fatty acid methyl ester (FAME) conversion efficiencies, respectively. Highest fatty acid yielding feedstock were Jatropha and a novel non-edible Mediterranean crop, Cynara cardunculus, the microalgae Chlorella and Nannochloropsis, and the fungi/yeast Trichosporon oleaginosus, Rhodosporidium toruloides, Lipomyces starkeyi, Mortierella isbellina, and Pichia guilliermondi. For wet microalgal biomass, a preference for acid-catalysed direct transesterification was determined, while base-catalysed DT was more suitable for dry biomass, except for turbo-thin film-assisted DT of microalgal biomass. The data highlight that DT operational parameters and technologies need optimisation for feedstock and water content and outcomes may be strongly strain-dependent for microalgal feedstock. To bring commercial biodiesel potential of some high-yielding feedstock to reality, comprehensive life cycle – and techno-economic analyses are required for intensified and non-intensified DT processing, taking feedstock production and possibilities of biorefinery concepts into account whilst also focussing on those processing platforms that can esterify fatty acids in wet biomass.