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Abstract The unprecedented growth of computational capabilities in recent years has allowed Artificial Intelligence (AI) models to be developed for medical applications with remarkable results. However, a large number of Computer Aided Diagnosis (CAD) methods powered by AI have limited acceptance and adoption in the medical domain due to the typical blackbox nature of these AI models. Therefore, to facilitate the adoption of these AI models among the medical practitioners, the models' predictions must be explainable and interpretable. The emerging field of explainable AI (XAI) aims to justify the trustworthiness of these models' predictions. This work presents a systematic review of the literature reporting Alzheimer's disease (AD) detection using XAI that were communicated during the last decade. Research questions were carefully formulated to categorise AI models into different conceptual approaches (e.g., Post-hoc, Ante-hoc, Model-Agnostic, Model-Specific, Global, Local etc.) and frameworks (Local Interpretable Model-Agnostic Explanation or LIME, SHapley Additive exPlanations or SHAP, Gradient-weighted Class Activation Mapping or GradCAM, Layer-wise Relevance Propagation or LRP, etc.) of XAI. This categorisation provides broad coverage of the interpretation spectrum from intrinsic (e.g., Model-Specific, Ante-hoc models) to complex patterns (e.g., Model-Agnostic, Post-hoc models) and by taking local explanations to a global scope. Additionally, different forms of interpretations providing in-depth insight into the factors that support the clinical diagnosis of AD are also discussed. Finally, limitations, needs and open challenges of XAI research are outlined with possible prospects of their usage in AD detection.