The rapidly advancing domain of Explainable Artificial Intelligence (XAI) has sparked significant interests in developing techniques to make AI systems more transparent and understandable. Nevertheless, in real-world contexts, the methods of explainability and their evaluation strategies present numerous limitations.Moreover, the scope of responsible AI extends beyond just explainability. In this paper, we explore these limitations and discuss their implications in a boarder context of responsible AI when considering other important aspects, including privacy, fairness and contestability.