The Λ cold dark matter model successfully describes a wide range of cosmological observations. However, the persistent discrepancy between the value of the Hubble constant inferred from cosmic microwave background measurements within this model and that obtained from local distance-ladder determinations points to a significant inconsistency. This short review examines theoretical responses across the cosmological inference chain, from the gravitational field equations to the pre-recombination sound horizon and the late-time distance–redshift relation. We focus primarily on modified gravity, and briefly discuss early- and late-time mechanisms that can alter the acoustic ruler, distance measures, structure growth, or gravitational response. Current proposals can reduce the nominal tension, but often at the cost of correlated shifts in cosmic microwave background spectra, standard-ruler distances, lensing, structure growth, or calibrator information. Further progress requires unified likelihoods and multi-probe tests linking all key observables under the same model assumptions.