Biomass refers to plant-based materials that are not used for food or feed. As an energy source, lignocellulosic biomass (lignin, cellulose and hemicellulose) can be converted into various forms of biofuel using thermal, chemical and biochemical methods. Chemical conversion implies the use of solid catalysts, usually oxide materials. In this context, reducible oxides are considered to be more active than non-reducible oxides. But why? Using density functional theory DFT + U calculations with the inclusion of dispersion forces, we describe the properties of anatase TiO2, a reducible oxide, and tetragonal ZrO2, a non-reducible oxide, the (101) surfaces in this context. In particular, we focus on the role of surface reduction, either by direct creation of oxygen vacancies via O2 desorption, or by treatment in hydrogen. We show that the presence of reduced centres on the surface of titania or zirconia (either Ti3+ or Zr3+ ions, or oxygen vacancies) results in lower barriers and more stable intermediates in two key reactions in biomass catalytic conversion: ketonization of acetic acid (studied on ZrO2) and deoxygenation of phenol (studied on TiO2). We discuss the role of Ru nanoparticles in these processes, and in particular in favouring H2 dissociation and hydrogen spillover, which results in hydroxylated surfaces. We suggest that H2O desorption from the hydroxylated surfaces may be a relevant mechanism for the regeneration of oxygen vacancies, in particular on low-coordinated sites of oxide nanoparticles. Finally, we discuss the role of nanostructuring in favouring oxide reduction, by discussing the properties of ZrO2 nanoparticles of diameter of about 2 nm.This article is part of a discussion meeting issue 'Providing sustainable catalytic solutions for a rapidly changing world'.