This article reviews the partial hydrogenation of renewable polyunsaturated methyl esters of linseed, sunflower, Cynara cardunculus and soybean oils into their monounsaturated counterparts which is upgraded biodiesel fuel employing highly active and selective water-soluble rhodium, ruthenium and palladium TPPTS complexes and by water-dispersible palladium(0) nanoparticles stabilized by water-soluble nitrogen-containing ligands which possess even higher activities than those exhibited by Pd/TPPTS benchmark catalysts in aqueous/organic two-phase systems. Furthermore, this article presents a novel study on the full hydrogenation of polyunsaturated methyl esters of sunflower and palm kernel oils to obtain up to 99.0 mol% methyl stearate (MS) using water-soluble Rh- and Ru-TPPTS catalytic complexes under mild reaction conditions in aqueous/organic two-phase systems. The full hydrogenation reaction of polyunsaturated FAMEs into MS is an interesting catalytic reaction because MS is an industrial feedstock for the manufacture of specialties such as surfactants, emulsifiers, etc., and could also act as a model reaction for studying the full hydrogenation of edible oils to saturated fats to be further subjected to interesterification reactions with liquid edible vegetable oils to yield foodstuffs with zero amounts of trans-fats especially after publication of results of very recent investigations which have questioned whether there really are direct associations between saturated fat consumption and a higher cardiovascular disease risk. (C) 2014 Elsevier B.V. All rights reserved.