This work is a review for the progress of the scalar field dark matter (SFDM) hypothesis. Here we outline a possible brane world model justifying the hypothesis of the scalar field origin for the dark matter (DM). This model contains two branes, on one of the branes lives the matter of the standard model of particles but on the other one, only spin-0 fundamental interactions are present. In this model these spin-0 fields are the DM and maybe the dark energy (DE). Thus, DM and DE interact only through the gravitational force with the matter brane. Starting with this hypothesis, we write a Lagrangian where the dark matter is of scalar origin with a cosh scalar field potential. The scalar field with a cosh potential behaves exactly in the same way as dust at cosmological scales. In this sense the scalar field mimics very well cold dark matter (CDM). The free parameters of the Lagrangian can be fixed using cosmological observations. After fixing all the free parameters of the model, we found that a scalar field fluctuation collapses forming objects with a preferred mass of ~ 10¹² M. Nevertheless, at galactic scales there exist some strong differences with the CDM paradigm. The scalar field contains an effective pression which avoids the collapse of a scalar field fluctuation, implying that scalar field objects like galaxies contain a flat density profile in the center. This implies that the SFDM paradigm could resolve the cusp density profile problem of galaxies.