This book constitutes the refereed proceedings of the 13th International Conference on Unconventional Computation and Natural Computation, UCNC 2014, held in London, ON, Canada, in July 2014. The 31 revised full papers were carefully reviewed and selected from 79 submissions. The papers cover a wide range of topics including among others molecular, quantum, optical and chaos computing as well as neural computation, evolutionary computation, swarm intelligence and computational neuroscience.