Hydrodeoxygenation (HDO) is a key step in upgrading of biomass‐derived feedstocks to fuels and valuable chemicals. In this review, I select to discuss the current understanding of heterogeneous HDO catalysis of representative small oxygenates that are present in the bio‐crude obtained from thermochemical conversions of biomass raw materials, as the efficient valorization of these presently underutilized carbon sources would significantly improve carbon recovery and the overall process techno‐economics, in addition to facilitating downstream processing in some cases. A primary focus is laid on the kinetics, mechanisms and active site requirements of molecular H2‐involved hydrogenation and deoxygenation reactions of small aliphatic oxygenates. More often than not, surprising contrasts are found between gas‐solid and polar liquid‐solid interfaces and hint toward substantial restructuring and modifications of the catalytic surfaces and chemistries in polar liquids, particularly induced by protic molecules (the most abundant being water). Knowledge gaps, uncharted territories and associated challenges for the interrogations of these fundamental aspects are also discussed in this review.