The Hubble tension: A decade review

Ever since the new millennium, precision cosmology has forged the $\Lambda$-cold-dark-matter ($\Lambda$CDM) model as the standard model of concordant cosmology, withstanding various tests except for an ever-enlarging discrepancy between early-Universe observations and late-Universe measurements on the current Hubble expansion rate of our observable Universe. This Hubble-constant tension has likely become a real crisis for modern cosmology, with the discrepancy persisting regardless of whether the early-Universe observations depend on \textit{Planck} CMB or not, and the late-Universe measurements depend on distance ladders at all. If the Hubble tension originates from a different early Universe, its resolutions pertain to shrinking the sound horizon by altering either early expansion or recombination histories, but at the same time necessitating modifications to both primordial and late Universe altogether. Alternatively, if the Hubble tension arises from a different late Universe, its resolutions operate by changing the absolute magnitude of supernovae either intrinsically or effectively, both of which have been strongly constrained by the inverse distance ladders with the cosmic distance duality relation. The remaining options seem to turn to our local Universe, but a local Hubble bubble or cosmic void solution has long been ruled out as a significant contribution to the Hubble tension. In view of this dilemma, we review in this paper alternative resolutions involving interacting dark energy models, either combining early-time and late-time modifications or operating at the transition from inhomogeneity to homogeneity scales.