Explore the evolution and future of supercomputing software in this 42-minute webinar from the Society for Industrial and Applied Mathematics' Supercomputing Spotlights series. Delve into the impact of Moore's Law on high-performance computing (HPC), the challenges posed by its potential end, and innovative software solutions for emerging architectures. Learn about the shift from compute-centric to data locality-centric programming, the importance of efficient data movement, and the role of multicore and accelerator technologies. Discover the PADAL workshop series, techniques for optimizing sparse computations, and new execution models for GPUs and CPUs. Gain insights into stencil computation and the exciting future of computing, with a call for collaboration in addressing upcoming challenges in the field.