Thermal power plants are an important asset in the current energy infrastructure, delivering ancillary services, power, and heat to their respective consumers. Faults on critical components, such as large pumping systems, can lead to material damage and opportunity losses. Pumps plays an essential role in various industries and as such clever maintenance can ensure cost reductions and high availability. Prognostics and Health Management, PHM, is the study utilizing data to estimate the current and future conditions of a system. Within the field of PHM, Predictive Maintenance, PdM, has been gaining increased attention. Data-driven models can be built to estimate the remaining-useful-lifetime of complex systems that would be difficult to identify by man. With the increased attention that the Predictive Maintenance field is receiving, review papers become increasingly important to understand what research has been conducted and what challenges need to be addressed. This paper does so by initially conceptualising the PdM field. A structured overview of literature in regard to application within PdM is presented, before delving into the domain of thermal power plants and pump systems. Finally, related challenges and trends will be outlined. This paper finds that a large number of experimental data-driven models have been successfully deployed, but the PdM field would benefit from more industrial case studies. Furthermore, investigations into the scale-ability of models would benefit industries that are looking into large-scale implementations. Here, examining a method for automatic maintenance of the developed model will be of interest. This paper can be used to understand the PdM field as a broad concept but does also provide a niche understanding of the domain in focus.