Hydro Power plant (HPP), being one of the most convenient options for power generation, has been modelled considering very wide aspects of their application. A model is simply a mathematical representation of a system and it may serve different purposes like dynamic simulation of hydro power, energy systems modelling involving policy making, condition monitoring, etc. The purpose of modelling HPPs may lead to various kind of models for a single Hydropower. This paper aims at reviewing hydropower models developed using different methods along with the purpose for modelling them. This will provide brief insights about state of the art on hydropower modelling and its emerging techniques. Furthermore, this paper presents in more detail about tracking the advancements in dynamic models for classical and variable speed hydropower plants highlighting the need for the development of more accurate models. The work mainly involves narrative review of published works on hydro power modelling techniques. Also, it includes systematic reviews about dynamic representation of hydropower plants. As this paper aims at presentation of hydro power models in a classified manner based on purpose of modelling, the areas of improvement in each type of model have been discussed. Models for control can be made to be more accurate by including more realistic featured like penstock dynamics, uncertainties, etc which further help in design of advanced control systems. There are several potential benefits of HPP modelling, such as optimizing plant performance, improving control, reducing maintenance costs, and enhancing overall system efficiency and reliability.