The current best explanation for all of the observational evidence is a "cold dark matter" (CDM) theory, where the dark matter is composed of "WIMPs" (weakly interacting massive particles). Neutrinos are WIMPs that we know exist, and compose some small fraction of dark matter, but neutrinos are "hot", they travel at relativistic speeds, rather than much slower speeds.
There have been many theories of what the "unseen mass" could have been made of before the CDM/WIMP theory gained ground, but those competing theories have been eliminated by observational evidence which contradicts their predicted effects. Large amounts of dust would block visible light and impose characteristic changes on the light that passes through it. We see dust in other galaxies and our own, but we don't not see nearly enough dust in the right locations and in the right quantities to account for the missing mass. So it can't be dust. Large gas clouds are another idea. Huge, transparent, whispy clouds of gas. But these too would affect the light passing through them, adding the spectral absorption signature of the gas to the light coming from the other side of the cloud. We can observe several large concentrations of gas around galaxies, and often the mass of that gas is larger than the total mass of stars in the galaxy, but it's still far too low, by an order of magnitude or more, to be the missing mass. We also see cases, such as the bullet cluster, where we can map the location of the stars, gas, and the overall mass (through gravitational lensing), and we see that the mass is not where the gas is. Another theory is that it could be not dust but bigger chunks of stuff, like planets or brown dwarfs, so called "MaCHOs" (Massive Compact Halo Objects). But to make up the missing mass there would have to be a great many of them. We can collect statistics on how common such objects are in our own galaxy and nearby galaxies using gravitational micro-lensing surveys. Because there are a huge number of stars in the sky, and if there were lots of MaCHOs floating around then every once in a while one would happen to be precisely lined up along the line of sight to another star and that arrangement would slightly brighten the remote star. We can monitor a huge number of stars using modern digital imaging systems and survey the MaCHO population this way. We've found several such micro-lensing events but again the observations put an upper limit on the MaCHO population which is far, far below what could possibly account for all of the missing mass.
No matter how you slice the observations, you still end up with a lot of missing mass and a lot of inconsistent observations. Unless you accept the possibility of WIMP dark matter. When you do that then all of the observations fall into place. Not just the above but also things like the large scale structure of the universe, the structure of the cosmic microwave background radiation, and so forth.