The possible presence of invisible but gravitating dark matter has been studied already almost hundred years. First attempts to derive the total density of matter in the Solar vicinity were made by Öpik (1915), Kapteyn (1922), Jeans (1922), and Oort (1932). Results were different: Öpik (1915), Kapteyn (1922) and Oort (1932) found that the total density of matter can be explained by known stellar populations, if a reasonable extrapolation of faint dwarf stars is taken into account. In contrast, Jeans (1922) found that there must be two dark stars to each bright star. This discussion continued until the end of 20th century.
A much larger discrepancy between the masses of visible objects and the total masses of stellar systems they belong to, was discovered by Zwicky (1933). He concluded that, in order to hold galaxies together in the cluster, the cluster must contain huge amounts of dark (invisible) matter.
Initially no distinction between local dark matter in the solar vicinity and global dark matter in clusters of galaxies was made. The realisation, that these two types of dark matter have very different properties and nature came from the detailed study of galactic models (Einasto 1974).
In this talk I have used my recent review of the dark matter (Einasto 2009).