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The Association CiE is promoting the development, particularly in Europe, of computability-related science, ranging over mathematics, computer science, and applications in various natural and engineering sciences such as physics and biology. This also includes the promotion of the study of philosophy and history of computing as it relates to questions of computability. It chiefly does so by organizing the conference series Computability in Europe, by editing the Association journal Computability, and by editing a book series Theory and Applications of Computability.

The Association was founded in Athens in the year 2008. Its current president is Professor Elvira Mayordomo (Zaragoza, Spain).

The CiE conference takes place yearly, with the first meeting in the series being organized in 2005 in Amsterdam – The Netherlands. The conference is coordinated by a Steering Committee, currently headed by Dr. Florin Manea (Göttingen, Germany).

The first issue of the Computability journal appeared in 2012, as an answer to the interest of the participants of the CiE conferences and the members of the CiE Association for a journal that is entirely devoted to the subject of computability and all its multidisciplinary facets. Since then, two issues of the journal were published every year. The current Editor-in-Chief is Professor Vasco Brattka (Munich, Germany and Cape Town, South Africa).