Despite being very different in nature, martingales and rough paths have many similarities and their interplay is most fruitful. As a concrete example, I will introduce the recent notion of rough stochastic differential equations and explain its importance in filtering, pathwise control theory and option pricing under (possibly rough) stochastic volatility. (Joint work with numerous people, including Pavel Zorin-Kranich, Khoa Lê, Antoine Hocquet, Peter Bank, Christian Bayer and Luca Pelizzari.)