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This is a brief review on the history of the Bose-Einstein condensate (BEC)or boson star model of galactic dark matter halos, where ultra-light scalardark matter particles condense in a single BEC quantum state. The halos can bedescribed as a self-gravitating, possibly self-interacting, coherent scalarfield.  On a scale larger than galaxies, dark matter behaves like cold dark matterwhile below that scale the quantum mechanical nature suppresses the dark matterstructure formation due to the minimum length scale determined by the mass$m\st{>}{\sim}10^{-24} eV$ and the self-interaction of the particles. Thisproperty could alleviate the cusp problem and missing satellite problems of the$\Lambda$CDM model. Furthermore, this model well reproduces the observedrotation curves of spiral and dwarf galaxies, which makes the model promising.

Is dark matter a BEC or scalar field?