CiE aims to widen understanding and appreciation of the importance of the concepts and techniques of computability theory, and to support the development of a multi-disciplinary community of researchers focused on computability-related topics.

The ACiE positions itself at the interface between applied and fundamental research, prioritising mathematical approaches to computational barriers.

Former members of the Council of the Association are: Alison Pease and Olivier Bournez (Past Membership Secretary).

In memory of the visionary engagement of its founding president, the association established the S. Barry Cooper Prize honouring a researcher who has contributed to a broad understanding and foundational study of computability by outstanding results, by seminal and lasting theory building, by exceptional service to the research communities involved, or by a combination of these.

[8] The current chair of the Steering Committee of the conference series is Florin Manea; his predecessors were Benedikt Löwe (2005–2013) and Arnold Beckmann (2013–2016).