Artificial Intelligence (AI) models have reached a very significant level of accuracy. While their superior performance offers considerable benefits, their inherent complexity often decreases human trust, which slows their application in high-risk decision-making domains, such as finance. The field of eXplainable AI (XAI) seeks to bridge this gap, aiming to make AI models more understandable. This survey, focusing on published work from the past five years, categorizes XAI approaches that predict financial time series. In this paper, explainability and interpretability are distinguished, emphasizing the need to treat these concepts separately as they are not applied the same way in practice. Through clear definitions, a rigorous taxonomy of XAI approaches, a complementary characterization, and examples of XAI's application in the finance industry, this paper provides a comprehensive view of XAI's current role in finance. It can also serve as a guide for selecting the most appropriate XAI approach for future applications.