Modelling and Simulation (M&S) offer adequate abstractions to manage the complexity of analysing big data in scientific and engineering domains. Unfortunately, big data problems are often not easily amenable to efficient and effective use of High Performance Computing (HPC) facilities and technologies. Furthermore, M&S communities typically lack the detailed expertise required to exploit the full potential of HPC solutions while HPC specialists may not be fully aware of specific modelling and simulation requirements and applications. The COST Action IC1406 High-Performance Modelling and Simulation for Big Data Applications has created a strategic framework to foster interaction between M&S experts from various application domains on the one hand and HPC experts on the other hand to develop effective solutions for big data applications. One of the tangible outcomes of the COST Action is a collection of case studies from various computing domains. Each case study brought together both HPC and M&S experts, giving witness of the effective cross-pollination facilitated by the COST Action. In this introductory article we argue why joining forces between M&S and HPC communities is both timely in the big data era and crucial for success in many application domains. Moreover, we provide an overview on the state of the art in the various research areas concerned.