This book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general, as well as the future of High Performance Computing systems and heterogeneous architectures. The contributions cover a broad range of topics, from improved system management to Computational Fluid Dynamics, High Performance Data Analytics, and novel mathematical approaches for large-scale systems. In addition, they explore innovative fields like coupled multi-physics and multi-scale simulations. All contributions are based on selected papers presented at the 26th and 28th Workshops on Sustained Simulation Performance, held at the High Performance Computing Center, University of Stuttgart, Germany, in October 2017 and 2018, and the 27th and 29th Workshops on Sustained Simulation Performance, held at the Cyberscience Center, Tohoku University, Japan, in March 2018 and 2019.