Power transformers are a key component of electrical networks, and they are both expensive and difficult to upgrade in a live network. Many utilities monitor the condition of the components that make up a power transformer and use this information to minimize the outage and extend the service life. Routine and diagnostic tests are currently used for condition monitoring and appraising the ageing and defects of the core, windings, bushings and tap changers of power transformers. To accurately assess the remaining life and failure probability, methods have been developed to correlate results from different routine and diagnostic tests. This paper reviews established tests such as dissolved gas analysis, oil characteristic tests, dielectric response, frequency response analysis, partial discharge, infrared thermograph test, turns ratio, power factor, transformer contact resistance, and insulation resistance measurements. It also considers the methods widely used for health index, lifetime estimation, and probability of failure. The authors also highlight the strengths and limitations of currently available methods. This paper summarizes a wide range of techniques drawn from industry and academic sources and contrasts them in a unified frame work.