The strong CP problem is the Standard Model fine-tuning with the cleanest measurement behind it. QCD's Lagrangian admits a CP-violating term governed by the parameter theta-bar, and nothing in the theory prefers any value for it; order unity would be natural. Yet a nonzero theta-bar gives the neutron an electric dipole moment, and decades of increasingly exquisite EDM experiments constrain |theta-bar| below 10^-10 (Peccei and Quinn 1977 framing the problem; current limits via the neutron EDM program).
A dimensionless parameter ten orders of magnitude smaller than natural, protected by no symmetry, demands explanation, and the field's favorite, the Peccei-Quinn mechanism promoting theta-bar to a dynamical field that relaxes to zero, predicts the axion: hunted for four decades without detection, and increasingly cornered. Post-inflationary axion models face domain-wall overproduction and quality problems, pre-inflationary ones face isocurvature constraints, and the remaining parameter space narrows with each haloscope generation (Lu et al. 2024). The axion's second job, serving as the dark matter, doubles the stakes of the continuing null results.
The standing is a forty-year-old fine-tuning whose standard solution is running out of room: ADMX and its successors are scanning the surviving mass windows, and either the axion appears or particle physics needs a different answer for why the strong force respects a symmetry nothing enforces.