The field of High Energy Physics needs a new jump at the Energy frontier. The answer to some of the more profound questions including the fundamental microscopic origin of the electroweak symmetry breaking, of Dark Matter, of the Baryon/Anti-Baryon asymmetry, and more, might be around the corner. After recent technological advances in accelerator physics and the new interest of the theoretical and experimental HEP communities, the muon collider is emerging as the more compact and energy efficient future collider candidate for new physics explorations at the 10+ TeV scale. In this talk I review the reach of muon colliders on some motivated new physics scenarios with a particular emphasis in two cases: i) Minimal Dark Matter, where I look at the sensitivity of Higgsino- and Wino-like Dark Matter through disappearing tracks, and ii) Muonphilic forces hypothetically responsible for the muon g-2 anomaly.