The advances in Machine Learning (ML) in recent years have been both impressive and far-reaching. However, the deployment of ML models is still impaired by a lack of trust in how the best-performing ML models make predictions. The issue of lack of trust is even more acute in the uses of ML models in high-risk or safety-critical domains. eXplainable artificial intelligence (XAI) is at the core of ongoing efforts for delivering trustworthy AI. Unfortunately, XAI is riddled with critical misconceptions, that foster distrust instead of building trust. This paper details some of the most visible misconceptions in XAI, and shows how formal methods have been used, both to disprove those misconceptions, but also to devise practically effective alternatives.