The aim of this article is to highlight the theoretical underpinnings in the formation of media and digital competence in the use of AI. This topic is one that needs addressing due to the intensive development of AI technology, which is making an increasingly visible incursion into both private and professional life. There is no doubt that AI has also entered the education sector, becoming something of a game-changer in teaching and educational processes. This situation has therefore necessitated a change in the theoretical framework for digital and media literacy (DL&ML), which has been undergoing constant transformation in recent years due to the intensive development of AI-based software. This article reviews the most popular theoretical frameworks relating to the formation of skills and knowledge in the use of AI. Based on a comparison of DigComp 2.2, AI Literacy Competency Framework, AI literacy TPACK, The Machine Learning Education Framework, The UNESCO AI Competency Framework, it was noted that: 1) there is currently a lack of consensus on a clear definition of DL&ML areas and indicators in AI; 2) the vast majority of theoretical frameworks do not have their own research tools and rely on a high degree of flexibility to diagnose this DL&ML area depending on contextual considerations; 3) the current theoretical frameworks related to AI allow the measurement of DL&ML using qualitative approaches; 4) the theoretical frameworks defining DL&ML are changing with the development of AI; 5) the lack of explicitness in defining DL&ML makes it difficult to conduct longitudinal and comparative research; and 6) each of the theoretical frameworks analysed emphasises a different area of AI use and the anticipation of the consequences associated with it.