Appropriate maintenance of industrial equipment keeps production systems in good health and ensures the stability of production processes. In specific production sectors, such as the electrical power industry, equipment failures are rare but may lead to high costs and substantial economic losses not only for the power plant but for consumers and the larger society. Therefore, the power production industry relies on a variety of approaches to maintenance tasks, ranging from traditional solutions and engineering know-how to smart, AI-based analytics to avoid potential downtimes. This review shows the evolution of maintenance approaches to support maintenance planning, equipment monitoring and supervision. We present older techniques traditionally used in maintenance tasks and those that rely on IT analytics to automate tasks and perform the inference process for failure detection. We analyze prognostics and health-management techniques in detail, including their requirements, advantages and limitations. The review focuses on the power-generation sector. However, some of the issues addressed are common to other industries. The article also presents concepts and solutions that utilize emerging technologies related to Industry 4.0, touching on prescriptive analysis, Big Data and the Internet of Things. The primary motivation and purpose of the article are to present the existing practices and classic methods used by engineers, as well as modern approaches drawing from Artificial Intelligence and the concept of Industry 4.0. The summary of existing practices and the state of the art in the area of predictive maintenance provides two benefits. On the one hand, it leads to improving processes by matching existing tools and methods. On the other hand, it shows researchers potential directions for further analysis and new developments.