Safe operation of complex structures and machines cannot be achieved by visual inspections alone. Thus, simple, efficient and cost-effective inspection methods are of paramount importance. This review article is aimed at providing an insight into approaches of health monitoring and condition monitoring of structures and machines based on machine learning. Machine learning is an approach of using data to construct predictive models giving predictions of existing and future trends. In the case of structural health monitoring and condition monitoring of machinery, it is able to detect damage and distinguish between different damage types and severities, thus being able to provide early warnings of failure of structural and machinery components. In this review paper, the focus is on information obtained from time-frequency features, which provides an advantage with respect to features in time domain and frequency domain of tracking changes of structural integrity in time, which is especially useful in dealing with non-stationary signals. Details of damage-sensitive feature extraction, data analysis and decision making are provided.