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Here we review the recent research activities on the epitaxial growth of semiconductor nanowires (NWs) on graphene substrates. Semiconductor NWs with quasi one‐dimensional structure have become an active research field due to their various interesting physical properties and potentials for future electronic and optoelectronic device applications, such as transistors, sensors, solar cells, light emitting diodes, and lasers. At almost the same time graphene, a two‐dimensional material made of carbon, was discovered and has gained an ever increasing interest during the last few years owing to its remarkable properties, including excellent electrical conductivity, optical transparency, and mechanical strength and flexibility. A hybrid structure by epitaxially growing semiconductor NWs on graphene could provide a new avenue for the development of future advanced NW‐based flexible electronic and optoelectronic devices. We address the challenges for the growth of semiconductor NWs on graphene, with a special focus on the III–V semiconductors, and highlight some potential applications of the NW/graphene hybrid system. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) Part of Focus Issue on “Semiconductor Nanowires” (Eds.: Chennupati Jagadish, Lutz Geelhaar, Silvija Gradecak) Epitaxial growth of semiconductor nanowires on graphene is an emerging research field for the development of next‐generation flexible electronic and optoelectronic hybrid devices. This article reviews the recent developments in the growth of various semiconductor nanowires and the device applications of the nanowire/graphene hybrid systems. [ABSTRACT FROM AUTHOR]