This paper is dedicated to modelling rotating machine signals as cyclostationary processes, with strong emphasis on the peculiarities and pitfalls that this issue implies. The objective is to demonstrate that machine signals require specific processing that are much more subtle than for communication signals—from which the paradigm of cyclostationarity was originally issued from and developed for. First, different types of cyclostationarity embracing a multitude of rotating machine signals are distinguished. In particular, the importance of considering pure rather than impure cyclostationarity is stressed out. Next, the relationships between angle and time cyclostationarity are investigated and some useful results are derived. It is shown that vibration signals exhibit cyclostationarity if and only if the random speed fluctuation of the machine is periodic, stationary or cyclostationary. Finally, a comprehensive methodology is proposed for processing actual cyclostationary signals: three typical examples dealing with vibration signals of an IC engine, a gearbox and a rolling element bearing are presented, each of them being characterised by a different type of cyclostationarity. The methodology proposed in this paper is general enough and may serve as a guideline for modelling and analysing other types of rotating machine signals, such as pressure signals, electric signals, etc.