The goal of this work is to describe how robots interact with complex city environments, and to identify the main characteristics of an emerging field that we call Robot-City Interaction (RCI). Given the central role recently gained by modern cities as use cases for the deployment of advanced technologies, and the advancements achieved in the robotics field in recent years, we assume that there is an increasing interest both in integrating robots in urban ecosystems, and in studying how they can interact and benefit from each others. Therefore, our challenge becomes to verify the emergence of such area, to assess its current state and to identify the main characteristics, core themes and research challenges associated with it. This is achieved by reviewing a preliminary body of work contributing to this area, which we classify and analyze according to an analytical framework including a set of key dimensions for the area of RCI. Such review not only serves as a preliminary state-of-the-art in the area, but also allows us to identify the main characteristics of RCI and its research landscape.