The critical interplay between Artificial Intelligence (AI) and Trust is investigated in this work. This interplay has profound interdisciplinary implications as it is linked to the adoption of AI systems and services in society. With the increasing influence that AI has on finance, transportation, communication, healthcare, etc., trust in the new technology is pivotal. This work carries out a systematic computational literature review and identifies the major topics that are portrayed when it comes to the interplay of AI and trust. The corpus consists of 34786 publications from Web of Science and Scopus scientific databases. The 91 identified topics reveal the multi-faceted nature and dynamic relation of trust and AI that is scattered across technical, social, and ethical dimensions. The ranking of the topics, the similarity analysis, and the hierarchical clustering in conjunction with critical discussions reveal additional insights. Especially aspects of governance, security, and explainability along several application domains such as healthcare, robotics, financial sector, transportation, etc. emerge. The acquired insights offer value to researchers in the area, businesses, regulatory bodies, and policymakers. The results shed light on the importance of the interplay of trust and AI and point out the broader implications across domains that need to be appropriately addressed.