In this talk I will illustrate with two examples (Higgsino dark matter and Exotic Higgs decays) how electron-proton colliders present unique opportunities to probe BSM scenarios where proton-proton colliders fall short due to the experimental difficulties in reconstructing the signal due to the large hadronic backgrounds. The \emph{leit-motiv} of these examples are long-lived particles (LLPs), which have received recently a lot of attention from both the experimental and theoretical communities. We find that the proposed $e^-p$ colliders can be competitive against their more energetic $pp$ incarnations for lifetimes between a millimeter and a micron, depending on the physics scenario under consideration.