A review of the development of the concept of dark matter is given. I begin the review with the description of the discovery of the mass paradox in our Galaxy and in clusters of galaxies. In mid 1970s the amount of observational data was sufficient to suggest the presence of a massive and invisible population around galaxies and in clusters of galaxies. The nature of the dark population was not clear at that time, but the hypotheses of stellar as well as of gaseous nature of the new population had serious difficulties. These difficulties disappeared when non-baryonic nature of dark matter was suggested in early 1980s. In addition to the presence of Dark Matter, recent observations suggest the presence of Dark Energy, which together with Dark Matter and ordinary baryonic matter makes the total matter/energy density of the Universe equal to the critical cosmological density. There are various hypothesis as for the nature of the dark matter particles, and generally some form of weakly interactive massive particles (WIMPs) are strongly favored. Both Dark Matter and Dark Energy are the greatest challenges for modern physics since their nature is unknown.
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