Interest is rapidly growing in the potential of high-energy muon colliders as an innovative platform for future particle physics research. These colliders offer distinct features in the study of Higgs boson properties and serve as a robust high-energy lepton collider. This seminar will present several of my recent developments in understanding the unique capabilities of muon colliders for investigating phenomena beyond the Standard Model, including but not limited to the Higgs mechanism, dark matter, and issues related to naturalness.