Galaxies move as if mass is missing
Stars and gas in galaxies orbit faster at large radii than visible matter alone predicts under standard gravity. Galaxy clusters show the same problem on larger scales.
Lensing maps invisible mass
Gravitational lensing measures total mass regardless of whether it shines. Systems such as the Bullet Cluster show mass distributions displaced from much of the hot ordinary gas, a pattern difficult to explain with baryonic matter alone.
The early Universe also points the same way
Cosmic-microwave-background structure and the growth of large-scale cosmic structure are successfully modelled with a substantial non-baryonic matter component.
The particle hunt is still empty
Direct-detection experiments such as LZ have pushed sensitivity to extremely low interaction rates without a confirmed signal. That eliminates parts of parameter space rather than eliminating dark matter itself.
Research record
NASA Webb — Bullet Cluster mass mappingNASA · open sourceESA Planck — publications and cosmology resultsESA · open sourceBerkeley Lab — LZ direct-detection limitsInstitutional · open sourceWhat Is the Evidence for Dark Matter?
Direct answer: The gravitational evidence for an unseen matter component is strong, but the microscopic identity of that component is unknown.
Strong phenomenon, unknown particle. Modified-gravity ideas remain scientifically testable alternatives but must reproduce the full cosmological and lensing evidence.