Black holes are gravitational objects predicted by general theory of relativity as a result of absolute gravitational collapse of matter. One of their interesting feature is that they are completely described by only few parameters in a final state, despite of precise process and matter from which they were formed. This theoretical result has become known as hypothesis: ,,black holes have no hair”, where hair is every field associated with black hole that contribute to the surface integral in spacelike infinity (analog to the Gauss integral in electrostatics). Big contribution to the topic was given by theorems about uniqueness of Schwarzschild spacetime as static, spherically symmetric, asimptotically flat vacuum solution of Einstein’s equations, and Reissner-N¨ordstrom, in the presence of electromagnetic field. The same is true fot Kerr and Kerr-Newman solutions in stationary case. First proofs of above hypothesis were Bekenstein’s proofs which excluded existence of wide range of fields around static and stationary black holes. Soon was shown the importance of included assumptions and that black hole hair can exist if some of them were omitted. General conditions for (non)existence of hair became unsettled. In this work we have gone in detail through Bekenstein’s theorems and gave review of existing hair and their characteristics. Lower bound on ’hair length’ is among them. While proved for fairly general case, it’s still violated in some models. It’s important to note on which assumptions are based no-hair theorems. In most cases, one of them is equivalence of symmetry between matter fields and metric. Leaving it out, sometimes we can find hair. We have analyzed possible symmetry non-inheritance of scalar fields. In the end we pointed to possible testing with ongoing experiments, which would also test general relativity and could lead to finding new fields in nature.