Research in the field of social robotics is allowing service robots to operate in environments with people. In the aim of realizing the vision of humans and robots coexisting in the same environment, several solutions have been proposed to (1) perceive persons and objects in the immediate environment; (2) predict the movements of humans; as well as (3) plan the navigation in agreement with socially accepted rules. In this work, we discuss the different aspects related to social navigation in the context of our experience in an indoor environment. We describe state-of-the-art approaches and experiment with existing methods to analyze their performance in practice. From this study, we gather first-hand insights into the limitations of current solutions and identify possible research directions to address the open challenges. In particular, this paper focuses on topics related to perception at the hardware and application levels, including 2D and 3D sensors, geometric and mainly semantic mapping, the prediction of people trajectories (physics-, pattern- and planning-based), and social navigation (reactive and predictive) in indoor environments.