Black holes (BHs) in general relativity (GR) are very simple objects. This property, that goes under the name of `no-hair’, has been refined in the last few decades and admits several versions. The simplicity of BHs makes them ideal testbeds of fundamental physics and of GR itself. Here we discuss the no-hair property of BHs, how it can be measured in the electromagnetic or gravitational window, and what it can possibly tell us about our Universe.