The advance of composites used in aerospace, civil and biomechanical engineering and other technology branches over the last decades has led to a substantial increase in the application of these materials. In addition, the search for new and improved materials in aerospace industry has stimulated the development of hybrid materials partly made out of composites, such as Fibre-Metal Laminates (FMLs). These materials are composed of alternatively stacked aluminium and fibre-reinforced composite layers such that the best features of both constituents are combined. FMLs also have additional advantages over conventional monolithic aluminium alloys and fibre-reinforced composites, such as an excellent fatigue and damage-tolerance behaviour. Furthermore, this class of materials possesses good fire, impact, damping, insulation and corrosion-resistance properties.To ensure a maximal reliability under service conditions, the failure mechanisms of FMLs must be well understood. The main mesoscale failure mechanisms that endanger their overall reliability are delamination between adjacent plies, cracking, and plasticity in individual metal layers. Important failure mechanisms at the microscale are debonding of fibres, fibre breakage, pull-out of broken fibres and crack growth in the epoxy matrix.Finite element simulations serve as an important tool for understanding the mechanical failure behaviour of FMLs in engineering applications. However, the performance of a direct numerical analysis of an engineering structure (e.g., an aircraft wing), where all features of the underlying heterogeneous microstructure are accounted for explicitly, requires an extremely fine finite element mesh and thus an impractical amount of computational time. A more efficient approach is to study engineering structures with the aid of mesoscale material models that account for the underlying microstructure in an average sense. The average properties in the mesoscale model can be computed using a numerical homogenization approach, where the microstructural stresses and deformations are averaged over a representative material volume. The present thesis comprises a detailed study of the failure behaviour of fibre-metal laminates at the meso- and microscale levels, and proposes a numerical homogenization framework that links specific failure mechanisms at these two levels of observation.