This paper presents a robust computational model for the response of composite laminates to high intensity transverse dynamic loading emanating from local impact by a projectile and distributed pressure pulse due to a blast. Delaminations are modeled using a cohesive type tie-break interface introduced between sublaminates while intralaminar damage mechanisms within the sublaminates are captured in a smeared manner using a strain-softening plastic-damage model. In the latter case, a nonlocal regularization scheme is used to address the spurious mesh dependency and mesh-orientation problems that occur with all local strain-softening type constitutive models. The results for the predicted damage patterns using the nonlocal approach are encouraging and qualitatively agree with the experimental observations. The predictive performance of the proposed numerical model is assessed through comparisons with available instrumented impact test results on a class of carbon-fiber reinforced polymer (CFRP) composite laminates. Force-time histories and other derived cross-plots such as the force versus projectile displacement and progression of projectile energy loss as a function of time are compared with available experimental results to demonstrate the efficacy of the model in capturing the details of the dynamic response. Another case study involving the blast loading of CFRP composite laminates is used to further highlight the capability of the proposed model in simulating the global structural response of composite laminates subjected to distributed pressure pulses.