This paper reviews ten years of work on the “Hubble tension” — a growing disagreement about how fast the Universe is expanding today. Measurements that use the early Universe, in particular fits to the cosmic microwave background (CMB) seen by the Planck satellite, give a Hubble constant H0 ≈ 67 km/s/Mpc. Direct, late‑time measurements anchored to nearby distance indicators such as Cepheid stars and Type Ia supernovae give higher values around 73 km/s/Mpc. The difference has grown with time and can reach a formal significance of about 5σ between Planck (67.27 ± 0.60 km/s/Mpc) and the SH0ES team (73.04 ± 1.04 km/s/Mpc), or even larger when other data sets are combined (for example 7.1σ with a Local Distance Network value of 73.50 ± 0.81 km/s/Mpc reported in the review). The authors frame this as a pressing crisis for the standard cosmological model, ΛCDM (Lambda cold dark matter), because the discrepancy appears regardless of which particular early‑ or late‑time data are used.

As a review article, the paper does not present new measurements. Instead it collects and organizes the observational status and the many proposed theoretical fixes. The authors separate the discussion into early‑Universe solutions, late‑Universe solutions, and options that link both. They describe a series of arguments they call “no‑go theorems,” which show that simple changes restricted only to the early Universe or only to the late Universe are hard to make consistent with all data. The review pays particular attention to the physical reason the tension appears and to which observational constraints restrict possible fixes.

Early‑Universe proposals aim to change the scale imprinted in the CMB and in baryon acoustic oscillations known as the sound horizon. The sound horizon is the distance that pressure waves in the early hot plasma could travel before photons decoupled — it sets a standard ruler for many cosmological measurements. Shrinking that ruler can raise the inferred H0 from early‑time data. To do that, models typically alter the pre‑recombination expansion history or the physics of recombination (when electrons combined with protons to form neutral atoms). The review emphasizes that successful early‑time models often also need to alter the primordial conditions (from inflation) and to address other tensions in late‑time structure measurements, so an early‑only fix is difficult to arrange.