Vegetable oil-based feeds are regarded as an alternative source for the production of fuels and chemicals. Paraffins and olefins can be produced from these feeds through catalytic deoxygenation. The fundamentals of this process are mostly studied by using model compounds such as fatty acids, fatty acid esters, and specific triglycerides because of their structural similarity to vegetable oils. In this Review we discuss the impact of feedstock, reaction conditions, and nature of the catalyst on the reaction pathways of the deoxygenation of vegetable oils and its derivatives. As such, we conclude on the suitability of model compounds for this reaction. It is shown that the type of catalyst has a significant effect on the deoxygenation pathway, that is, group 10 metal catalysts are active in decarbonylation/decarboxylation whereas metal sulfide catalysts are more selective to hydrodeoxygenation. Deoxygenation studies performed under H2 showed similar pathways for fatty acids, fatty acid esters, triglycerides, and vegetable oils, as mostly deoxygenation occurs indirectly via the formation of fatty acids. Deoxygenation in the absence of H2 results in significant differences in reaction pathways and selectivities depending on the feedstock. Additionally, using unsaturated feedstocks under inert gas results in a high selectivity to undesired reactions such as cracking and the formation of heavies. Therefore, addition of H2 is proposed to be essential for the catalytic deoxygenation of vegetable oil feeds.