The large availability of biomass, which, for the sake of decarbonization, is not supposed to be disposed of by burning and energy recovery, has led to the increasing production of polymer composites containing biomass-derived materials. The automotive industry is a field which, due to large production volumes and the requirements for safety, has large economic and environmental value. Despite this, the introduction of lignocellulosic fiber composites and generally biopolymers into this sector has been slow and so far mostly limited to non-structural or semi-structural components. This review critically considers the difficulties associated with the production of bumpers with biomass-derived materials and reports on a variety of fibers and polymers that have been proposed and on the equally variable degree of success of these studies. We also report on the understanding that rethinking the bumper in terms of materials could be an effective way to introduce biomass-based materials into the whole automotive sector on a larger scale with increased benefits.