Explainable Artificial Intelligence (XAI) aims to help human decision makers in understanding the operation of complex AI models. However, many XAI solutions, based on non-symbolic methods, offer no formal guarantees and can produce erroneous results. In contrast, logic-based XAI guarantees the rigor of computed explanations, and this is paramount in high-stakes uses of AI. This talk overviews several flagship applications of Boolean satisfiability (SAT) solvers in reasoning about logic-based explanations.