Human-technology interaction deals with trust as an inevitable requirement for user acceptance. As the applications of artificial intelligence (AI) and robotics emerge and with their ever-growing socio-economic influence in various fields of research and practice, there is an imminent need to study trust in such systems. With the opaque work mechanism of AI-based systems and the prospect of intelligent robots as workers' companions, context-specific interdisciplinary studies on trust are key in increasing their adoption. Through a thorough systematic literature review on (1) trust in AI and robotics (AIR) and (2) AIR applications in the architecture, engineering, and construction (AEC) industry, this study identifies common trust dimensions in the literature and uses them to organize the paper. Furthermore, the connections of the identified dimensions to the existing and potential AEC applications are determined and discussed. Finally, major future directions on trustworthy AI and robotics in AEC research and practice are outlined.