A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

The Muon Collider is one of the most promising future collider facilities with the potential to reach multi-TeV center-of-mass energy and high luminosity. Due to the significant Higgs boson production cross section in muon-antimuon collisions at such high energies, the collider offers an excellent opportunity for in-depth exploration of Higgs boson properties. It holds the capability to significantly advance our understanding of the Higgs sector to a very high level of precision. However, the presence of beam-induced background resulting from the decay of the beam muons poses unique challenges for detector development and event reconstruction. In this paper, the prospects for measuring various Higgs boson properties at a center-of-mass energy of 3 TeV are presented, using a detailed detector simulation in a realistic environment. The study demonstrates the feasibility of achieving high precision results with the current state-of-the-art detector design. In addition, the paper discusses the detector requirements necessary to achieve this level of accuracy.

A multi-TeV muon collider produces a significant amount of Higgs bosons allowing for precise measurements of its couplings to Standard Model fundamental particles. Moreover, Higgs boson pairs are produced with a relevant cross-section, allowing for the determination of the second term of the Higgs potential by measuring the double Higgs production cross-section and therefore the trilinear self-coupling term. This contribution aims to give an overview of the Higgs measurement accuracies expected for the initial stage of the muon collider at $\sqrt{s}=3\mathrm{TeV}$ with an integrated luminosity of $1a{b}^{-1}$ and for the target center-of-mass energy at $10\mathrm{TeV}$ with $10a{b}^{-1}$ integrated luminosity. The results are obtained using the full detector simulations which include both physical and machine backgrounds.

Muon collisions are considered a promising means for exploring the energy frontier, leading to a detailed study of the possible feasibility challenges. Beam intensities of the order of ${10}^{12}$ muons per bunch are needed to achieve the necessary luminosity, generating a high flux of secondary and tertiary particles from muons decay that reach both the machine elements and the detector region. To limit the impact of this background on the physics performance, tungsten shieldings have been studied. A machine learning-based approach to the geometry optimization of these shieldings will be discussed.

A multi-TeV Muon Collider produces a significant amount of Higgs bosons allowing precise measurements of its couplings to Standard Model fundamental particles. Moreover, Higgs boson pairs are produced with a relevant cross-section, allowing the determination of the second term of the Higgs potential by measuring the double Higgs production cross section and therefore the trilinear self-coupling term. This contribution aims to give an overview of the Higgs measurements accuracies expected for the initial stage of the Muon Collider at s=3TeV with an integrated luminosity of 1ab−1 and for the target center-of-mass energy at 10TeV with 10ab−1 integrated luminosity. The results are obtained using the full detector simulations which include both physical and machine backgrounds.