Biodiesel is synthesized via the transesterification of lipid feedstocks with low molecular weight alcohols. Currently, alkaline bases are used to catalyze the reaction. These catalysts require anhydrous conditions and feedstocks with low levels of free fatty acids (FFAs). Inexpensive feedstocks containing high levels of FFAs cannot be directly used with the base catalysts currently employed. Strong liquid acid catalysts are less sensitive to FFAs and can simultaneously conduct esterification and transesterification. However, they are slower and necessitate higher reaction temperatures. Nonetheless, acid-catalyzed processes could produce biodiesel from low-cost feedstocks, lowering production costs. Better yet, if solid acid catalysts could replace liquid acids, the corrosion and environmental problems associated with them could be avoided and product purification protocols reduced, significantly simplifying biodiesel production and reducing cost. This article reviews some of the research related to biodiesel production using acid catalysts, including solid acids.