Appropriate Trust in Artificial Intelligence (AI) systems has rapidly become an important area of focus for both researchers and practitioners. Various approaches have been used to achieve it, such as confidence scores, explanations, trustworthiness cues, or uncertainty communication. However, a comprehensive understanding of the field is lacking due to the diversity of perspectives arising from various backgrounds that influence it and the lack of a single definition for appropriate trust. To investigate this topic, this paper presents a systematic review to identify current practices in building appropriate trust, different ways to measure it, types of tasks used, and potential challenges associated with it. We also propose a Belief, Intentions, and Actions (BIA) mapping to study commonalities and differences in the concepts related to appropriate trust by (a) describing the existing disagreements on defining appropriate trust, and (b) providing an overview of the concepts and definitions related to appropriate trust in AI from the existing literature. Finally, the challenges identified in studying appropriate trust are discussed, and observations are summarized as current trends, potential gaps, and research opportunities for future work. Overall, the paper provides insights into the complex concept of appropriate trust in human-AI interaction and presents research opportunities to advance our understanding on this topic.@en