The history of the study of dark matter in the Universe is briefly reviewed at first, showing that weakly interacting particle relicts of the big-bang triggered the formation of galaxies, and an extended halo of these particles dominates the gravitational dynamics of the galaxies. The study of the dark-matter halo surrounding our Milky Way Galaxy is particularly useful, not only as a template for other systems, but more specifically in the context of various experiments attempting to detect these particles. In this colloquium, we present a recent study in which important constraints on phase-space structure of the halo is derived. Theoretical models of the halo are constructed keeping in mind that the visible matter in the form of stars and gas not only act as tracers of the gravitational potential of the Galaxy but contribute to it, dominantly at small galactocentric distances below ~5 kiloparsecs, and diminishing in importance progressively at larger distances where dark matter is the main contributor. The self-consistent model is compared with the observations of the rotation curve of the Galaxy, which is measured up to ~20 kpc. The constraints at larger distances are derived form the investigations of dynamics of dwarf-spheroidal galaxies, with particular reference to their susceptibility to tidal break-up in the gravitational potential of the dark matter halo. The self-consistent model reproduces the observed rotation curve of the Galaxy, the distance distribution of the dwarf-spheroidals and yields DM 0.3 Gev/cm3, 1/2DM > 350km s-1, rhalo > 150 kpc and MDM,halo~ 1012 Msun. The import of these determinations on the detection of DM halo dark matter particles constituting the halo is pointed out.