  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 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.
