Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and shastic discrete and continuous dynamical systems.