Scalar fields are ubiquitous in beyond the standard model particle physics. Simultaneously they have been suggested in gravitational physics to model for instance, dark energy or dark matter. In this talk I shall consider the status of scalar fields interacting with black holes and explain why it is in general hard to find equilibrium solutions of stationary black holes with a non-trivial scalar field profile (without non-minimal couplings). But I will also present a new type of exact solution to Einstein's equations minimally coupled to a massive complex scalar field describing rotating black holes with scalar hair. Some properties of this new type of solutions will be discussed together with some possible phenomenological implications.

References:

Asymptotically flat black holes with scalar hair: a review 
Carlos A. R. Herdeiro, Eugen Radu
e-Print: arXiv:1504.08209

Construction and physical properties of Kerr black holes with scalar hair
Carlos Herdeiro, Eugen Radu 
e-Print: arXiv:1501.04319

Kerr black holes with scalar hair
Carlos A. R. Herdeiro, Eugen Radu 
Phys.Rev.Lett. 112 (2014) 221101