Review of searches for rare processes and physics beyond the Standard Model at HERA

The electron–proton collisions collected by the H1 and ZEUS experiments at HERA comprise a unique particle physics data set, and a comprehensive range of measurements has been performed to provide new insight into the structure of the proton. The high centre of mass energy at HERA has also allowed rare processes to be studied, including the production of W and $$Z^{0}$$Z0 bosons and events with multiple leptons in the final state. The data have also opened up a new domain to searches for physics beyond the Standard Model including contact interactions, leptoquarks, excited fermions and a number of supersymmetric models. This review presents a summary of such results, where the analyses reported correspond to an integrated luminosity of up to 1 fb$$^{-1}$$-1, representing the complete data set recorded by the H1 and ZEUS experiments.