Furfural hydrogenation to furfuryl alcohol is an industrially significant reaction for biomass valorization. The hydrogenation process has been mainly catalyzed by chromite-based materials that are notorious for their toxicity, thereby highlighting the need to find alternate catalyst materials. In addition, there is a gap in the mechanistic understanding of furfural hydrogenation on transition metal surfaces. Herein, we combine density functional theory calculations and microkinetic modeling to study the reaction mechanism of furfural hydrogenation to furfuryl alcohol on terrace (111/0001) and stepped (211) transition metal surfaces. We find the rate- determining steps for furfural hydrogenation to depend on the identity of the metal, where the strong binding metals are limited by desorption of the product (furfuryl alcohol) while the moderate and weak binding metals are limited by steps involving surface hydrogenation or H2 activation. We show that the binding energy of furfural is a good descriptor to rationalize and predict the activity trends for the production of furfuryl alcohol. Among the metal and bulk/single atom alloy surfaces investigated in this work, we find Cu-based alloys to be the most active catalysts, with CuNi alloys predicted to be promising candidates for furfural hydrogenation.