Biodiesel is a non-toxic, drop-in liquid transportation fuel that is amenable to continuous production from sustainable biomass resources using catalytic technologies. A diverse range of catalysts and reactor technologies have been experimentally investigated and computationally modelled, for producing biodiesel (fatty acid methyl esters) from oil feedstocks by their esterification or transesterification with short-chain alcohols. Solid-acid and base catalysts are attractive for biodiesel production from renewable oil feedstocks due to their ease of separation from the desired biodiesel and glycerol by-product, use of Earth’s abundant elements, and suitability in continuous processes. Here, we review the technical challenges and opportunities in designing catalytic reactor systems for biodiesel production.