In this paper, we present a taxonomic review of the literature devoted to the use of operations research approaches for the design and operation of biomass feedstock supply chains (BFSCs). A total of 185 publications that have appeared from 1989 to 2017 are classified based on (1) the embedded optimisation subproblems; (2) the modelling methodologies used for their formulations; and (3) the methods employed for their solution. Our objective of using this classification scheme is to highlight the presence of some useful substructures in a BFSC problem that can, then, be exploited in developing its solution procedure. We illustrate this idea on some generic BFSC problems and present a Dantzig-Wolfe decomposition-based methodology for developing customised approaches to effectively tackle these difficult and large-sized BFSC problems. Finally, we suggest several promising future research directions.