A muon collider of 3, 6, or 10 TeV is considered one of the most interesting collider options at the energy frontier in HEP. In this talk I will present the collider concept and elucidate its discovery potential with a focus on some prime examples, like anomalous mass generation mechanisms for muons, Z' bosons and heavy neutral leptons. The main part of the talk will be devoted to the precision calculation and simulation of physics processes at a muon collider, especially collinear factorization within the full electroweak SM, electroweak NLO corrections and electroweak Sudakov factors.