Cellular foams are a modern class of materials with unique mechanical properties that have wide ranging engineering applications, in the areas of biomedical, acoustic and thermal insulation, and crashworthiness. Recently, foam materials have received increased attention for vehicle crashworthiness due to their lightweight and excellent energy absorption capabilities that allow significant weight reduction without compromising structural safety aspects. Accordingly, this paper reviews the crush and energy absorption behaviour of foam-filled structures that can be used for crashworthy design in transport engineering. In addition, the mechanical and dynamic properties of cellular material and their role on the crashworthiness performance of filled structure are discussed. Particularly, the influences of foam density and interactions, between the foam and the tubes, on the deformation mode of the filled structures are clarified. The advantages offered by the innovative foam material, which contains a density gradient, on the crashworthiness behaviour are also highlighted. Also, a brief summary of optimisation studies involving the use of foam-filled structures are presented. It was found that the cellular materials improve the crashworthiness performance when they are used as filler material in thin-walled energy absorbers due to their capability of altering the deformation mode to a more favourable one.