Multi-agent systems have been a core research topic in artificial intelligence for several decades. A multiagent system consists of multiple decision-making agents -which may be software-based AI systems, physicallyembodied robots, or humans -which must interact in a shared environment in pursuit of their goals. Multi-agent systems research spans a range of technical problems, such as how to design planning and learning algorithms which enable agents to achieve their goals; how to design multi-agent systems to incentivise certain behaviours in agents; how information is communicated and propagated among agents; and how norms, conventions, and roles may emerge in multi-agent systems. A vast array of applications have been addressed using multi-agent methodologies, including autonomous driving, multi-robot factories, automated trading, commercial games, automated tutoring, and robotic rescue teams.The purpose of this special issue is to showcase current multi-agent systems research led by university and industry groups based in the United Kingdom. Research groups and institutes in the UK which have significant activity in multi-agent systems research were invited to submit an article describing: (1) the technical problems in multi-agent systems tackled by the group (their core research agenda), including applications and industry collaboration; (2) the main approaches developed by the group and any key results achieved; and (3) important open challenges in multi-agent systems research from the perspective of the group.A large number of high-quality submissions were received, of which 14 were included for publication in the special issue. These articles represent a broad set of research topics within the field of multi-agent systems, showcasing the strength of contributions made by UK-based research groups in both universities and industry. We believe the open research problems discussed in each of the articles will provide a rich resource for researchers in this field, both new and old.Research groups from the following organisations are represented in the special issue (ordered alphabetically