Collider physics is rich, diverse, and versatile. Over the last several decades, colliders have played a central role in the experimental establishment of the Standard Model (SM), from the discovery of the charm quark in 1974 to the Higgs boson discovery in 2012 at the LHC. New colliders are necessary to shed light on the existence and nature of new physics. Per-mille level measurements of Higgs couplings to other particles of the SM may reveal that the scale of new physics beyond the SM is at the O(10)-TeV scale. The Cool Copper Collider, an attractive compact and power-efficient electron-positron machine, is capable of making per-mille-level measurements of Higgs couplings. The C3 relies on innovative power delivery to the C-band copper linac structure that is kept at liquid-nitrogen temperature, enabling accelerating gradients of over 120 MeV/m, resulting in a small collider footprint. A 10-TeV scale Muon Collider (MC) presents a highly attractive future collider option due to its small size and high luminosity for a low power budget. In this talk, I will present both C3 and MC, reviewing associated technological challenges as we outline a path forward.