Research on the relationship between affect and cognition in Artificial Intelligence in Education (AIEd) brings an important dimension to our understanding of how learning occurs and how it can be facilitated. Emotions are crucial to learning, but their nature, the conditions under which they occur, and their exact impact on learning for different learners in diverse contexts still needs to be mapped out. The study of affect during learning can be challenging, because emotions are subjective, fleeting phenomena that are often difficult for learners to report accurately and for observers to perceive reliably. Context forms an integral part of learners' affect and the study thereof. This review provides a synthesis of the current knowledge elicitation methods that are used to aid the study of learners' affect and to inform the design of intelligent technologies for learning. Advantages and disadvantages of the specific methods are discussed along with their respective potential for enhancing research in this area, and issues related to the interpretation of data that emerges as the result of their use. References to related research are also provided together with illustrative examples of where the individual methods have been used in the past. Therefore, this review is intended as a resource for methodological decision making for those who want to study emotions and their antecedents in AIEd contexts, i.e. where the aim is to inform the design and implementation of an intelligent learning environment or to evaluate its use and educational efficacy.