Esterification and transesterification methods, systems and apparatus are disclosed which increase the efficiency of esterification reactions. The methods comprising utilizing an annular gap reactor comprises a rotor rotating within a stator to provide an annular flow passage comprising a flow path containing a high-shear treatment zone in which the passage spacing is smaller than in the remainder of the zone to provide a subsidiary higher-shear treatment zone. In exemplary embodiments, the reactor is modified to include an evaporator portion including an opening in the stator near the end of the reactor and a series of fins placed in the opening. Increase in the rates due to the annular gap reactor allow for the use of less catalyst, poorer catalysts, lower temperature and reduction in unwanted side reactions at more economically favorable conditions.