This review paper summarizes the current state-of-the-art of the chemical transformation of oils/fats (i.e., triacylglycerols) to the use of biofuels or bio-lubricants in the means of transport, which is a novelty. The chemical transformation is necessary to obtain products that are more usable with properties corresponding to fuels synthesized from crude oil. Two types of fuels are described—biodiesel (the mixture of methyl esters produced by transesterification) and green diesel (paraffins produced by hydrogenation of oils). Moreover, three bio-lubricant synthesis methods are described. The transformation, which is usually catalysed, depends on: (i) the type and composition of the raw material, including alcohols for biodiesel production and hydrogen for green diesel; (ii) the type of the catalyst in the case of catalysed reactions; (iii) the reaction conditions; and (iv) types of final products. The most important catalysts, especially heterogeneous and including reaction conditions, for each product are described. The properties of biodiesel and green diesel and a comparison with diesel from crude oil are also discussed.