Our current understanding of the mechanisms underlying pedestrian flows in crowded, hurried and scary situations is insufficient for their effective control. The same holds for traffic management on our busy roads.Accurate mathematical models are continuously developed  to describe and predict these situations. Both off-line (assessment of new infrastructure and network designs) and on-line application (e.g. real-time prediction and control) of these models require accurate and robust  computational methods that can provide timely simulation of human and vehicle traffic flows.  For example, real-time estimation and prediction of crowds require fast numerical solution methods for non-linear partial differential equations. These models can be used iteratively to optimize evacuation plans and crowd-management schemes, or can be used for data assimilation. State-of-the-art approaches entail generalisations of the classical Godunov scheme,  Lagrangian schemes, and hybrid algorithms combining continuum  and  high-end microscopic models. In a similar fashion, optimisation of vehicular flow in complex freeway and urban networks requires high-end computational models, which can be used for a variety of problems, including but not limited to real-time traffic management and the optimisation of evacuation instructions.  Uncertainty quantification is pivotal in modeling such problems, since many contributing factors are uncertain by their very nature (e.g. the occurrence of an incident, the dynamics of a disaster), adding severely to the (computational) complexity of the optimisation problem. Computational Science and Engineering is expected to contribute significantly to solving these issues allowing for future advanced large-scale applications of network traffic flows.