The accumulation of greenhouse gases in the atmosphere resulting from the extensive use of fossil fuels and the depletion of oil reserves due to the increasing demands for energy compel the progressive replacement of fossil fuels by renewable energy sources among which biomass. Triglycerides-based biomass such as plant oils, animal fats, waste cooking and micro-algal oils should be upgraded by transesterification, cracking/hydrocracking and selective deoxygenation (SDO) to provide, respectively, biodiesel (fatty acid methyl esters), the so-called organic liquid product (mixture of hydrocarbons in the range of gasoline, kerosene and diesel) and green diesel (hydrocarbons in the diesel range). Problems related to the production, storage and use of the already produced biodiesel shifts the research to the second and third upgrading route. Intensive work in the last ten years has shown that the noble metals (mainly palladium) and the NiMo, CoMo and NiW sulphide catalysts supported on high surface area carriers, are promising concerning SDO for producing green diesel in the context of a stand-alone process of natural triglycerides. However, the high cost of the noble metal catalysts and the eventual S-contamination of the end product when using the aforementioned sulfided catalysts have rise intensive parallel research in the last three years for developing low cost Ni-based non-sulphide catalysts. The research effort in this area seems to focus on the following issues: (i) effect of supports, nickel loading and promoters on the catalytic performance of Ni-based non-sulphide catalysts, (ii) SDO pathways over these catalysts, (iii) effect of preparation method on their catalytic performance, (iv) comparison of nickel catalysts with other metallic and sulphide catalysts, (v) development of nickel phosphide catalysts, (vi) development of NiMo, CoMo or NiW non-sulphide catalysts (reduced, carbides, nitrides) and (vii) deoxygenation in low or no hydrogen containing atmosphere. In the present article we critically review the contributions relevant to each one of the aforementioned subjects for obtaining a synthetic picture concerning the progress pointed out so far and the future perspectives as well. (C) 2015 Elsevier B.V. All rights reserved.