In this talk, I will discuss some of the major open questions in particle physics and make the case that they can be very well addressed by a qualitatively new type of particle accelerator: a high-energy muon collider. Recent progress on long-standing accelerator and detector challenges makes such a collider a compelling successor to the LHC. Special attention will be paid to the role the Higgs will play at a multi-TeV muon collider. We will also discuss some unique, complementary opportunities for studying Deep Inelastic Scattering at Muon Ion collider or searches for new physics with a beam dump experiment.
