This book constitutes the refereed proceedings of the 15th Conference on Computability in Europe, CiE 2019, held in Durham, UK, in July 2019. The 20 revised full papers presented were carefully reviewed and selected from 35 submissions. In addition, this volume includes 7 invited papers. The conference CiE 2018 had the following six special sessions: computational neuroscience, history and philosophy of computing, lowness notions in computability, probabilistic programming and higher-order computation, smoothed and probabilistic analysis of algorithms, and transnite computations.