There are 2 prevailing theories for dark matter candidates.
"WIMPs", and "MACHOs",
Or, Weaking Interacting Massive Particles, and Massive Compact Halo Objects.
Wimps would be things like neutrinos, or neutron radiation clouds.
Machos would be something more like dense clouds of matter of an unknown type that concentrates in the halo around galaxies.
There are some on-going experiments to attempt to measure the ambient neutrino flux in space away from terrestrial sources of them, to see if neutrinos can account for the extra mass observed, but so far neutrino flux alone isn't able to explain things like the bullet cluster.
IIRC, a resent meta-analyis study of satellite tellemetry patterns suggest that the earth has a halo of dark matter as well, but I don't have a link handy.
Essentially though "dark matter" is an apellation applied to a phenomenon that has been observed distantly in places like the previously mentioned bullet cluster, but also has pronouned and measurable influence on our own milky way galaxy's shape and rotational properties. The observable matter in both locations is insufficient to explain the kinds of rotational and gravitational system effects we are observing. "Dark matter" is a kind of place holder to explain the incongruity. At the moment, nobody really knows for certain exactly what it is, but we can infer some of its properties. It appears to not interact with light, so it must be electromagnetically neutral, and it clearly has mass. That's about all we do know.