Most accurate machine learning models unfortunately produce black-box predictions, for which it is impossible to grasp the internal logic that leads to a specific decision. Unfolding the logic of such black-box models is of increasing importance, especially when they are used in sensitive decision-making processes. In thisworkwe focus on forests of decision trees, which may include hundreds to thousands of decision trees to produce accurate predictions. Such complexity raises the need of developing explanations for the predictions generated by large forests.We propose a post hoc explanation method of large forests, named GAM-based Explanation of Forests (GEF), which builds a Generalized Additive Model (GAM) able to explain, both locally and globally, the impact on the predictions of a limited set of features and feature interactions.We evaluate GEF over both synthetic and real-world datasets and show that GEF can create a GAM model with high fidelity by analyzing the given forest only and without using any further information, not even the initial training dataset.