In this thesis, the damage mechanisms and failure behaviour of four scaled laminated carbon fibre composite plates under transverse loading '(low-velocity impact and static indentation) and subsequent compression after impact/indentation loading were investigated by highly-detailed experiments, high-fidelity finite element modelling and simple analytical methods. Interrupted static indentation tests with the use of X-ray CT-scans at different damage stages helped to study the damage evolution and interaction between inter- and intra-laminar damages during impact and indentation. Finite element models with interface elements and user defined constitutive model were embedded into regions inside and between plies to model matrix cracks and delaminations. The predictive capabilities were validated by the detailed experimental results both qualitatively and quantitatively. The models were able to accurately predict the individual damage modes as well as the damage mode interaction. The scaling effects and geometric nonlinear response associated with delamination propagation during impact/indentation were observed and modelled by nonlinear analytical solutions. The damage sequence and failure behaviour of laminates under compression after impact were also studied via experiments and finite element modelling including the key driving damage mechanisms. Possible solutions for reducing the computational cost of deploying the developed high-fidelity finite element models were provided. These solutions were validated and shown to be advantageous for capturing the overall response and damage prediction for large and complex composite structures.