Trust is long recognized to be an important factor in Recommender Systems (RS). However, there are different perspectives on trust and different ways to evaluate it. Moreover, a link between trust and transparency is often assumed but not always further investigated. In this paper we first go through different understandings and measurements of trust in the AI and RS community, such as demonstrated and perceived trust. We then review the relationsships between trust and transparency, as well as mental models, and investigate different strategies to achieve transparency in RS such as explanation, exploration and exploranation (i.e., a combination of exploration and explanation). We identify a need for further studies to explore these concepts as well as the relationships between them.