The rapid advancement of artificial intelligence has led to significant improvements in automated decision-making. However, the increased performance of models often comes at the cost of explainability and transparency of their decision-making processes. In this paper, we investigate the capabilities of large language models to explain decisions, using football refereeing as a testing ground, given its decision complexity and subjectivity. We introduce the EXplainable Video Assistant Referee System, X-VARS, a multi-modal large language model designed for understanding football videos from the point of view of a referee. X-VARS can perform a multitude of tasks, including video description, question answering, action recognition, and conducting meaningful conversations based on video content and in accordance with the Laws of the Game for football referees. We validate X-VARS on our novel dataset, SoccerNet-XFoul, which consists of more than 22k videoquestion-answer triplets annotated by over 70 experienced football referees. Our experiments and human study illustrate the impressive capabilities of X-VARS in interpreting complex football clips. Furthermore, we highlight the potential of X-VARS to reach human performance and support football referees in the future. We will provide code, model, dataset, and demo upon publication.