  We consider the status of black hole solutions with non-trivial scalar fields
but no gauge fields, in four dimensional asymptotically flat space-times,
reviewing both classical results and recent developments. We start by providing
a simple illustration on the physical difference between black holes in
electro-vacuum and scalar-vacuum. Next, we review no-scalar-hair theorems. In
particular, we detail an influential theorem by Bekenstein and stress three key
assumptions: 1) the type of scalar field equation; 2) the spacetime symmetry
inheritance by the scalar field; 3) an energy condition. Then, we list regular
(on and outside the horizon), asymptotically flat BH solutions with scalar
hair, organizing them by the assumption which is violated in each case and
distinguishing primary from secondary hair. We provide a table summary of the
state of the art.
