Rolling-element bearing vibrations are random cyclostationary, that is they exhibit a cyclical behaviour of their statistical properties while the machine is operating. This property is so symptomatic when an incipient fault develops that it can be efficiently exploited for diagnostics. This paper gives a synthetic but comprehensive discussion about this issue. First, the cyclostationarity of bearing signals is proved from a simple phenomenological model. Once this property is established, the question is then addressed of which spectral quantity can adequately characterise such vibration signals. In this respect, the cyclic coherence - and its multi-dimensional extension in the case of multi-sensors measurements -- is shown to be twice optimal: first to evidence the presence of a fault in high levels of background noise, and second to return a relative measure of its severity. These advantages make it an appealing candidate to be used in adverse industrial environments. The use and interpretation of the proposed tool are then illustrated on actual industrial measurements, and a special attention is paid to describe the typical "cyclic spectral signatures" of inner race, outer race, and rolling-element faults.