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The rise of decision processes in various sectors has led to the adoption of decision support systems (DSSs) to support human decision-makers but the lack of transparency and interpretability of these systems has led to concerns about their reliability, accountability and fairness. Explainable Decision Support Systems (XDSS) have emerged as a promising solution to address these issues by providing explanatory meaning and interpretation to users about their decisions. These XDSSs play an important role in increasing transparency and confidence in automated decision-making. However, the increasing complexity of data processing and decision models presents computational challenges that need to be investigated. This review, therefore, focuses on exploring the computational complexity challenges associated with implementing explainable AI models in decision support systems. The motivations behind explainable AI were discussed, explanation methods and their computational complexities were analyzed, and trade-offs between complexity and interpretability were highlighted. This review provides insights into the current state-of-the-art computational complexity within explainable decision support systems and future research directions. [ABSTRACT FROM AUTHOR]