Due to agile developments in the field of robotics and human-robot interaction, prospective robotic agents are intended to play the role of teammates and partner with humans to perform operations, rather than tools that are replacing humans helping humans in a specific task. this notion of partnering with robots raises new challenges for human-robot interaction (HRI), which gives rise to a new field of research in HRI, namely human-robot trust. Where humans and robots are working as partners, the performance of the work can be diminished if humans do not trust robots appropriately. Considering the impact of human-robot trust observed in different HRI fields, many researchers have investigated the field of human-robot trust and examined various concerns related to human-robot trust. In this work, we review the past works on human-robot trust based on the research topics and discuss selected trends in this field. Based on these reviews, we finally propose some ideas and areas of potential future research at the end of this paper.