The calibration of phenomenological constitutive material models has been a constant need, because the parameters differ for each material and the ability of a model to mimic the real behaviour of a material is highly dependent on the quality of these parameters. Classically, the parameters of constitutive models are determined by standard tests under the assumption of homogeneous strain and stress fields in the zone of interest. However, in the last decade, Digital Image Correlation techniques and full-field measurements have enabled the development of new parameter identification strategies, such as the Finite Element Model Updating, the Constitutive Equation Gap Method, the Equilibrium Gap Method and the Virtual Fields Method. Although these new strategies have proven to be effective for linear and non-linear models, the implementation procedure for some of them is still a laborious task. The aim of this work is to give a detailed insight into the implementation aspects and validation of these methods. Detailed flowcharts of each strategy, focusing on the implementation aspects, are presented and their advantages and disadvantages are discussed. Moreover, these modern strategies are compared for the cases of homogeneous isotropic linear elasticity and isotropic plasticity with isotropic hardening. A simple numerical example is used to validate and compare the different strategies.