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Abstract Artificial Intelligence (AI) algorithms are increasingly providing decision making and operational support across multiple domains. AI includes a wide (and growing) library of algorithms that could be applied for different problems. One important notion for the adoption of AI algorithms into operational decision processes is the concept of assurance. The literature on assurance, unfortunately, conceals its outcomes within a tangled landscape of conflicting approaches, driven by contradicting motivations, assumptions, and intuitions. Accordingly, albeit a rising and novel area, this manuscript provides a systematic review of research works that are relevant to AI assurance, between years 1985 and 2021, and aims to provide a structured alternative to the landscape. A new AI assurance definition is adopted and presented, and assurance methods are contrasted and tabulated. Additionally, a ten-metric scoring system is developed and introduced to evaluate and compare existing methods. Lastly, in this manuscript, we provide foundational insights, discussions, future directions, a roadmap, and applicable recommendations for the development and deployment of AI assurance.