We are experiencing painful months, and as we write this editorial, the COVID-19 pandemic is still ongoing, severely affecting the peoples of many researchers who participated in this special issue. Our first thought is for the victims of this tragedy. Despite the difficulties, we have worked hard to keep in touch with the authors of the manuscripts, the anonymous referees, and the journal staff, so now we are especially delighted to present this special issue High-end Heterogeneous Architectures, Methodologies, and Algorithms (HHAMA-20) hosted on the Concurrency and Computation: Practice and Experience journal. The special issue collects an extension of the most valuable works presented at the Fifth Workshop on Models, Algorithms and Methodologies for Hybrid Parallelism in New HPC Systems (MAMHYP-19), held in Bialystok (Poland) in September 2019, jointly with the 13th Conference on Parallel Processing and Applied Mathematics (PPAM-19). 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. 1 CONTENTS OF THE SPECIAL ISSUE In this special issue, we collected nine papers, selected from 13 works submitted from eight different countries, with an acceptance rate of about 70%. Each manuscript has been accepted after two or three review rounds. In the first round, each paper has been assigned to two external anonymous reviewers. To the doubtful cases (i.e., borderline papers or with diverging recommendations), the guest editors of the special issue have been given additional individual attention. Authors of papers selected in the first round have been asked to revise their work according to the reviewers' feedback and submit a revised manuscript for a second or third review. The papers cover a broad spectrum of topics, and they could be classified into two large categories: