The field of extreme event attribution (EEA) has rapidly developed over the last two decades. Various methods have been developed and implemented, physical modelling capabilities have generally improved, the field of impact attribution has emerged, and assessments serve as a popular communication tool for conveying how climate change is influencing weather and climate events in the lived experience. However, a number of non-trivial challenges still remain that must be addressed by the community to secure further advancement of the field whilst ensuring scientific rigour and the appropriate use of attribution findings by stakeholders and associated applications. As part of a concept series commissioned by the World Climate Research Programme, this article discusses contemporary developments and challenges over six key domains relevant to EEA, and provides recommendations of where focus in the EEA field should be concentrated over the coming decade. These six domains are: (1) observations in the context of EEA; (2) extreme event definitions; (3) statistical methods; (4) physical modelling methods; (5) impact attribution; and (6) communication. Broadly, recommendations call for increased EEA assessments and capacity building, particularly for more vulnerable regions; contemporary guidelines for assessing the suitability of physical climate models; establishing best-practice methodologies for EEA on compound and record-shattering extremes; co-ordinated interdisciplinary engagement to develop scaffolding for impact attribution assessments and their suitability for use in broader applications; and increased and ongoing investment in EEA communication. To address these recommendations requires significant developments in multiple fields that either underpin (e.g., observations and monitoring; climate modelling) or are closely related to (e.g., compound and record-shattering events; climate impacts) EEA, as well as working consistently with experts outside of attribution and climate science more generally. However, if approached with investment, dedication, and coordination, tackling these challenges over the next decade will ensure robust EEA analysis, with tangible benefits to the broader global community.