Machine learning, a subfield of artificial intelligence, emphasizes the creation of algorithms capable of learning from data and generating predictions. However, in actuarial science, the interpretability of these models often presents challenges, raising concerns about their accuracy and reliability. Explainable artificial intelligence (XAI) has emerged to address these issues by facilitating the development of accurate and comprehensible models. This paper conducts a comparative analysis of various XAI approaches for tackling distinct data-driven insurance problems. The machine learning methods are evaluated based on their accuracy, employing the mean absolute error for regression problems and the accuracy metric for classification problems. Moreover, the interpretability of these methods is assessed through quantitative and qualitative measures of the explanations offered by each explainability technique. The findings reveal that the performance of different XAI methods varies depending on the particular insurance problem at hand. Our research underscores the significance of considering accuracy and interpretability when selecting a machine-learning approach for resolving data-driven insurance challenges. By developing accurate and comprehensible models, we can enhance the transparency and trustworthiness of the predictions generated by these models.