There is considerable interest in investigating the deoxygenation process, due to the high oxygen content of the feed-stocks used for the production of renewable fuels. This review addresses studies related to the catalytic hydrodeoxygenation of two feed-stocks (a) oils with high content of triglycerides and (b) oils derived from high pressure liquefaction or pyrolysis of biomass. Future research directions that could potentially bridge the existing gaps in these areas are provided.