At the time of designing structures up to date, the density and magnitude of the load have increased, and the requirements for regulation have also become more stringent. To ensure the essential requirements, especially the mechanical resistance and stability, the numerical modelling of the structure is carried out according to the current regulations. Due to various assumptions, idealization, discretization, and parameterizations that are introduced numerical modelling, obtained numerical model may not always reflect the actual structural behavior. It is known that these structures have a hidden resistance that can be determined by combining experimental investigations (static or/and dynamic tests) and finite element model updating methods to minimize the differences between the actual and predicted structural behavior. This paper provides a review of the FEMU process and methods used and summarizes the FEMU approach to help future engineers to select the appropriate method for solving some discussed issues. First, the main terms important for understanding FEMU are introduced. The whole process of model updating is described step by step: selection of updating parameters (design variables), definition of the model updating problem, its solution using different FEMU methods. An overview of the following methods is given: sensitivity-based, maximum likelihood, non-probabilistic, probabilistic, response surface and regularization methods. Each of the method is presented with the corresponding mathematical background, implementation steps, and examples of studies from the literature.