We present a general description of the scalar field dark matter (SFDM) hypothesis in the cosmological context. The scenario of structure formation under such a hypothesis is based on Jeans instabilities of fluctuations of the scalar field. It is shown that it is possible to form stable long lived objects consisting of a wide range of typical galactic masses around $10^{12}M_{\odot}$ once the parameters of the effective theory are fixed with the cosmological constraints. The energy density at the origin of such an object is smooth as it should.

9 pages, 12 eps figures. Invited talk, DARK 2002: 4th Heidelberg International Conference on Dark Matter in Astro and Particle Physics, 4-9 Feb 2002 Cape Town, South Africa