The drive toward greener process chemistry has stimulated the development of strong solid acids to replace traditional catalysts for efficient biodiesel production from free fatty acid (FFA) enriched biomass feedstocks. Notably, heterogeneous systems enable simple product isolation procedures and improve the catalyst recyclability. They may also be used in continuous reactors. Increasing interest is directed toward organic polymer-supported solid acid catalysts, holding the promise of easy incorporation of the catalyst into the support with high density and easy tuning of the support microstructure/morphology. In the present review, the focus is set on the most widely employed members of this class, including cation-exchange resins, micro- and mesoporous acidic resins, as well as supported acidic ionic liquids and ionomeric membranes. Moreover, we present the use of alternative organic polymer-based acidic catalysts (hybrid systerns). Attention is paid to correlations between parameters such as catalyst morphology, excess of alcohol required, FFA content in oil feedstock, presence of impurities and the performance of resin-supported acid catalysts, as well as to the catalyst recyclability. Finally, a brief survey illustrates the use of resin-supported acid catalysts for the preparation of biofuel additives alkyl levulinates - structurally quite similar to the biodiesel starting from biomass derived levulinic acid. (C) 2017 Elsevier Ltd. All rights reserved.