The Rule of Law is a foundational value of the modern democratic state. It contains within its most influential conceptualizations key legal principles to reduce arbitrariness in the exercise of power, and in doing so promoting legal certainty and individual autonomy, while protecting against despotism. A growing body of research points to the potential for AI to undermine Rule of Law values, especially when implemented in the exercise of public power. This talk concerns the attempt to translate these concerns into a conceptualization of how the Rule of Law can be used as a theoretical and operational foundation for a critical analysis of AI, assisting in structuring explorations into issues such as explainability, equality and democratic legitimacy.