“The nature of the dominant component of galaxies and clusters remains unknown.”
Source: Measuring the dark matter equation of state (Mon. Not. R. Astron. Soc. 415, L74–L77)
In the 1930s, astronomical observations of galaxy rotations showed that the outer regions were rotating (about the galaxy's 'centre') at the same speed, or faster, than the central regions. Subsequent calculations referring to the galaxy's mass, and thus its internal gravitational attractions, showed that if the outer regions were rotating at the observed speed, they would fly away from the centre and the galaxy would disintegrate.
As a means of explaining the anomaly, the idea of Dark Matter was proposed. For the explanation to work, the galaxies would have to be surrounded by a 'halo' of Dark Matter - a previously unknown form of matter that has mass, and yet does not interact with 'ordinary' matter in any other way than by gravity. Further calculations showed that for the galaxies to hold together, there would need to be approximately five times more Dark Matter (in terms of mass) than standard matter.
The current estimates are that Dark Matter accounts for 26.8% of the total matter in the universe. [ the rest being Dark Energy (68.3%) and visible matter (4.9%) ]
Since its proposal, various experimental projects have attempted to 'observe' dark matter [refs needed] - or more accurately its effects, as it would need to be 'invisible' to have escaped detection up until now. To date no experiment has been able to directly and unequivocally detect Dark Matter.
Alternative theories to explain the galaxy rotation enigma include the so-called MOND theory, which proposes that (the force of) gravity is not constant throughout the universe.
Further reading : Wikipedia
Note that of the 4.9% of 'ordinary matter' (a.k.a. 'Baryonic matter') only around 10% of that is currently accounted for. The so-called 'missing baryons' have now begun to be observed according to a 2017 paper published in arXiv Missing baryons in the cosmic web revealed by the Sunyaev-Zel'dovich effect