The continuous development of sport technologies constantly demands advancements in protective headgear to reduce the risk of head injuries. This article introduces new cellular helmet liner designs through two approaches. The first approach is the study of energy-absorbing biological materials. The second approach is the study of lattices comprised of force-diverting compliant mechanisms. On the one hand, bio-inspired liners are generated through the study of biological, hierarchical materials. An emphasis is given on structures in nature that serve similar concussion-reducing functions as a helmet liner. Inspiration is drawn from organic and skeletal structures. On the other hand, compliant mechanism lattice (CML)-based liners use topology optimization to synthesize rubber cellular unit cells with effective positive and negative Poisson's ratios. Three lattices are designed using different cellular unit cell arrangements, namely, all positive, all negative, and alternating effective Poisson's ratios. The proposed cellular (bio-inspired and CML-based) liners are embedded between two polycarbonate shells, thereby, replacing the traditional expanded polypropylene foam liner used in standard sport helmets. The cellular liners are analyzed through a series of 2D extruded ballistic impact simulations to determine the best performing liner topology and its corresponding rubber hardness. The cellular design with the best performance is compared against an expanded polypropylene foam liner in a 3D simulation to appraise its protection capabilities and verify that the 2D extruded design simulations scale to an effective 3D design.