This book constitutes the refereed proceedings of the 4th International Conference on Runtime Verification, RV 2013, held in Rennes, France, in September 2013. The 24 revised full papers presented together with 3 invited papers, 2 tool papers, and  6 tutorials were carefully reviewed and selected from 58 submissions. The papers address a wide range of specification languages and formalisms for traces; specification mining; program instrumentation; monitor construction techniques; logging, recording, and replay; fault detection, localization, recovery, and repair; program steering and adaptation; as well as metrics and statistical information gathering; combination of static and dynamic analyses and program execution visualization.