The mainstream [itex]\Lambda[/itex]CDM model has two types of Dark Matter, baryonic and non-baryonic DM.
The total amount of DM is about 27% of the total density, and therefore mass, of the universe. The Big Bang in the standard model can only produce about 4% of the total density as baryonic matter, mainly ordinary hydrogen and helium, (Note the visible baryonic matter, stars and nebulae, comprise only 0.3% of the total), and therefore about 23% of the total has to be some unknown non-baryonic species. Neutrinos, axions and other exotic particles have been candidates at one time or another.
There are a number of different types of observations: galaxy rotation curves, galaxy cluster dynamics, cluster gravitational lensing, large scale structure formation rates and the analysis of the CBM fluctuations, which is evidence that something is out there - but what?
Alternatively if all these observations are all to be explained by a modified theory of gravitation then that theory would have a mountain to climb, and explaining the Bullet Cluster is a particularly difficult case for such a theory.
Until the DM particle(s) have been identified in the laboratory (LHC?), their properties measured and found to be concordant with astronomical and cosmological constraints, we shall not really know what we are talking about.
For example, as another alternative, if the expansion rate of the early universe were different to that of the standard model, due to the action of some as yet unknown scalar field for example, then the amount of baryonic matter able to be produced in the BB would change and such a scenario might provide a third possibility; that all DM is in fact baryonic in nature. But then you would have to explain where it all is today and why it cannot be 'seen'!
The mainstream [itex]\Lambda[/itex]CDM model is the best thing we have going, at the moment.