Simulations are a widely used tool in the design and optimization of hydraulic systems and a crucial part of virtually representing a hydraulic system as part of digital twins of mobile machines. Typically, the basis of dynamic hydraulic system models are differential equations, derived from conservation laws, complemented with algebraic equations. However, physical effects like friction or fluid compressibility introduce complexity and lead to nonlinear behavior. Accurately capturing these dynamics makes the simulation of hydraulic systems challenging. Some of the parameters describing these equations, for example, diameters or other dimensions can be easily obtained from data sheets or other information provided by component manufacturers. Others may be completely unknown or must be chosen from a known value range. Determining the parameters may require detailed information, expert knowledge, or measurements from component test rigs. When deriving a digital twin for a specific machine from a production series of identical machines, modeling may also need to allow parameter variation for individual specific components, due to wear or the statistical variations occurring in the production process. This would lead to unfeasible effort when methods with manual parameter identification are used. Deploying a process to automatically parameterize the model with parameter identification methods could reduce the implementation effort. The aim of this paper is to review and analyze the possible methods for identifying unknown parameters or parameters that are not easily measurable in the application to fit lumped parameter hydraulic models of mobile machines to process data.