This new special edition illustrates the extent to which High-Performance Computing has become essential to both research and industry: modelling the climate, brain activity, the effectiveness of medical treatments, propagation of seismic waves, dispersion of pollutants in the atmosphere, nuclear fusion, depollution of water and oil exploration are just a few examples of the simulations discussed in this special issue, which are dependent on advances in supercomputing, both in terms of hardware and software, whether to increase computing capacity, to minimise energy consumption, or to put to good use multi-core architectures and hybrid micro-processor technologies.