<p>In this paper, we describe and investigate the Explainable Artificial Intelligence (XAI) methods based on the Shapley value, one of the most well-known imputation concepts in cooperative game theory, which is used to estimate the importance of features when building statistical and machine learning models. In cooperative games, the Shapley value provides a distribution of coalition payoff among players, and it becomes the basis of many methods that allocate the overall model performance among features. We describe the algorithms of the Feature Importance (FI), Permutation Feature Importance, and LIME methods, which do not use game-theoretic ideas in their basis, and the Shapley value-based methods: SHAP, KernelSHAP, SamplingSHAP, FastSHAP, and ShapG. We run the experiments on five datasets, two of which are high-dimensional and contain more than 100 features. We analyse the quality of the explanation results given by different XAI methods and their running time. Recommendations are given for the choice of an appropriate XAI method depending on the type of statistical or machine learning model to be explained, required running time, and the quality of the explanation results.</p>