The trend of lightweighting in many industry sectors leads to the need to balance reduced material mass with structural integrity. An important class of material often used for lightweighting is cellular solids. Their high strength and stiffness at low density offer a significant advantage in structural design. These materials can be manufactured as ordered trusses or as materials (lattices) with a less ordered structure. The drawback of lattice structures is the presence of geometrical flaws, which can affect its bulk mechanical behaviour. This research focuses on the understanding of fracture of lattice structures and its sensitivity to geometrical imperfections, through a combination of topological optimisation, experimental characterisation of mechanical properties, theoretical modelling of damage mechanisms, and materials design.