The landscape of high-performance computing (HPC) has been expanding with new technologies and increased system complexity. For hardware, this trend is driven by technological inventions increasing computing power capabilities while taming cost metrics. For applications, we are witnessing increasing growth in algorithms' complexity to accommodate constantly expanding data sizes and take full advantage of increasingly complex processing and storage characteristics. Successfully handling this expansion and maintaining performance and efficiency on adequate levels requires software that matches the emerging hardware and system innovations and can address concerns arising from evolving and new paradigms. An example of the evolving paradigms is heterogeneity-one of the most challenging properties of emerging parallel, distributed, and edge computing platforms. An appealing example of the new paradigms is a vigorous expansion of artificial intelligence (AI) and machine learning (ML) methods that have become pervasive in solving the most demanding problems across many science and engineering disciplines. Also, the approaching end of Moore's Law scaling requires exciting but complex innovations and advances in HPC hardware/software environments that need to be matched by advances in algorithms and software systems to meet the demands of the applications.The International Conference for Parallel Processing and Applied Mathematics (PPAM) has become, over the last 28 years, the premier forum for exchanging ideas between researchers involved in parallel and distributed computing, including theory and applications, as well as applied and computational mathematics. Thirteen previous events have been held in different universities in Poland since 1994, when the first PPAM took place in Czestochowa.The works presented at the PPAM 2022 covered topics demonstrating the increased diversity of the HPC ecosystem and the clear need for innovative solutions in this area. The wide range of topics includes enabling technologies for next-generation HPC systems, along with heterogeneous computing, quantum computing and communication; exploitation of parallel, distributed, and edge computing; algorithms for efficient problem solving on emerging HPC systems; programming paradigms and tools for HPC systems; scheduling and load balancing for parallel computing; modeling, characterization, and optimization for next-generation HPC systems; applications and software engineering for HPC platforms; methods and tools for the parallel solution of large-scale problems, including AI-and ML-based techniques. This special issue of Concurrency and Computation: Practice and Experience contains eight selected papers from the PPAM 2022 Conference.We hope you find them interesting and that they stimulate new ideas and future advancements in innovative technologies and models, algorithms, and software tools that facilitate efficient and convenient utilization of emerging HPC systems.