Recent technological advancements in small-scale unmanned aerial vehicles (UAVs) have led to the development of companion UAVs. Similar to conventional companion robots, companion UAVs have the potential to assist us in our daily lives and to help alleviating social loneliness issue. In contrast to ground companion robots, companion UAVs have the capability to fly and possess unique interaction characteristics. Our goals in this work are to have a bird's-eye view of the companion UAV works and to identify lessons learned and guidelines for the design of companion UAVs. We tackle two major challenges towards these goals, where we first use a coordinated way to gather top-quality human-drone interaction (HDI) papers from three sources, and then propose to use a perceptual map of UAVs to summarize current research efforts in HDI. While being simple, the proposed perceptual map can cover the efforts have been made to realize companion UAVs in a comprehensive manner and lead our discussion coherently. We also discuss patterns we noticed in the literature and some lessons learned throughout the review. In addition, we recommend several areas that are worth exploring and suggest a few guidelines to enhance HDI researches with companion UAVs.