The stellar-to-halo mass relation is galaxy formation's efficiency report: divide each galaxy's stellar mass by the mass of its inferred dark matter halo, and the resulting curve peaks at intermediate halo masses near 10^12 solar masses, falling steeply toward both smaller and larger halos, with even the most efficient systems converting only 10 to 20 percent of their available baryons into stars (Behroozi et al. 2013; Moster et al. 2018).
Every feature of the curve needs a separate story in ΛCDM. The low-mass decline is assigned to supernova feedback ejecting gas from shallow potentials; the high-mass decline to AGN feedback heating the gas of groups and clusters; the peak to the lucky mass where neither dominates; and the overall inefficiency to the combination. Each prescription is calibrated to the relation it explains rather than derived, and the assembled machine then fails at high redshift, where JWST finds galaxies whose stellar masses are far too large for the halos the standard relation assigns them, implying either that the relation evolves in ways the calibrations did not predict or that early star formation ran at efficiencies the feedback story forbids.
The standing is that the SHMR has become a fitting framework rather than a prediction, and its high-z extension is breaking. Euclid and Roman lensing-calibrated halo masses across environments and redshifts will measure the relation, and its scatter, well enough to test what the denominator actually is.