The reactive double bonds in conjugated vegetable oils are of high interest in industry. Traditionally, conjugated vegetable oils are added to paints, varnishes, and inks to improve their drying properties, while recently there is an increased interest in their use in the production of bioplastics. Besides the industrial applications, also food manufactures are interested in conjugated vegetable oils due to their various positive health effects. While the isomer type is less important for their industrial purposes, the beneficial health effects are mainly associated with the c9,t11, t10,c12 and t9,t11 CLA isomers. The production of CLA-enriched oils as additives in functional foods thus requires a high CLA isomer selectivity. Currently, CLAs are produced by conjugation of oils high in linoleic acid, for example soybean and safflower oil, using homogeneous bases. Although high CLA productivities and very high isomer selectivities are obtained, this process faces many ecological drawbacks. Moreover, CLA-enriched oils can not be produced directly with the homogeneous bases. Literature reports describe many catalytic processes to conjugate linoleic acid, linoleic acid methyl ester, and vegetable oils rich in linoleic acid: biocatalysts, for example enzymes and cells; metal catalysts, for example homogeneous metal complexes and heterogeneous catalysts; and photocatalysts. This Review discusses state-of-the-art catalytic processes in comparison with some new catalytic production routes. For each category of catalytic process, the CLA productivities and the CLA isomer selectivity are compared. Heterogeneous catalysis seems the most attractive approach for CLA production due to its easy recovery process, provided that the competing hydrogenation reaction is limited and the CLA production rate competes with the current homogeneous base catalysis. The most important criteria to obtain high CLA productivity and isomer selectivity are (1) absence of a hydrogen donor, (2) absence of catalyst acidity, (3) high metal dispersion, and (4) highly accessible pore architecture.