SummaryThis special issue on the Pervasive Nature of HPC (PN‐HPC) collects an extension of the most valuable works presented at the sixth Workshop on Models, Algorithms and Methodologies for Hybrid Parallelism in New HPC Systems (MAMHYP‐22), held in Gdansk (Poland) in September 2022, jointly with the 14th conference on Parallel Processing and Applied Mathematics (PPAM‐22). New original papers related to the workshop themes are also included. The final aim is to provide a glimpse of the current state of knowledge related to the development of efficient methodologies and algorithms for HPC systems with multiple forms of parallelism.