Recent literature underscores the need for teachers to develop AI competencies with a recognition of the current lack of well-defined competence frameworks. This critical review investigates teachers' Artificial Intelligence (AI) competence frameworks (AI CFTs), analysing their strengths, weaknesses and practical applications for researchers, educators and policymakers. It identifies five distinct types of AI CFTs within Competence Construct Claims (Child, S., & Shaw, S. 2023). A conceptual approach to validating competence frameworks. "Research Matters: A Cambridge University Press & Assessment publication," 35, 27-40.), each addressing the complexities of AI in its early stages. Notably, frameworks derived from empirical data offer detailed descriptions of competencies, while those based on conceptual models provide broader overviews. Highlighting the need for further empirical research, this review helps identify and understand existing approaches to teacher AI competence development and paves the way for integrating AI CFTs into teacher education, ultimately enhancing educators' preparedness to harness AI in their teaching practices.