Results of the last decade with respect to the selective hydrogenation of hydrocarbons with multiple unsaturation (dienes and alkynes) over heterogeneous palladium catalysts are reviewed. Factors such as metal dispersion, carbon deposits, and the use of promoters and additives controlling catalytic activities and chemo-, regio- and stereo-selectivity are discussed. A detailed treatment of the status of the selective removal of hydrocarbon impurities with multiple unsaturation from industrial feedstocks is also given.