Monitoring vibrations in rotating machinery allows effective diagnostics, as abnormal functioning states are related to specific patterns that can be extracted from vibration signals. Extensively studied issues concern the different methodologies used for carrying out the main phases (signal measurements, pre-processing and processing, feature selection, and fault diagnosis) of a malfunction automatic diagnosis. In addition, vibration-based condition monitoring has been applied to a number of different mechanical systems or components. In this review, a systematic study of the works related to the topic was carried out. A preliminary phase involved the analysis of the publication distribution, to understand what was the interest in studying the application of the method to the various rotating machineries, to identify the interest in the investigation of the main phases of the diagnostic process, and to identify the techniques mainly used for each single phase of the process. Subsequently, the different techniques of signal processing, feature selection, and diagnosis are analyzed in detail, highlighting their effectiveness as a function of the investigated aspects and of the results obtained in the various studies. The most significant research trends, as well as the main innovations related to the various phases of vibration-based condition monitoring, emerge from the review, and the conclusions provide hints for future ideas.