Due to the inability of GPS (or other GNSS methods) to provide satisfactory precision for the indoor location scenario, indoor positioning systems resort to other signals already available on-site, typically Wi-Fi given its ubiquity. However, instead of relying on an error-prone propagation model as in ranging methods, the popular fingerprinting positioning technique considers a more direct data-driven approach to the problem. First of all, the area of interest is divided into zones, and then a machine learning algorithm is trained to map between, for instance, power measurements (RSSI) from APs to the localization zone, thus effectively turning the problem into a classification one. However, although the positioning problem is a geometrical one, virtually all methods proposed in the literature disregard the underlying structure of the data, using generic machine learning algorithms. In this chapter we consider instead a graph-based learning method, Graph Neural Networks, a paradigm that has emerged in the last few years and that constitutes the state-of-the-art for several problems. After presenting the pertinent theoretical background, we discuss two possibilities to construct the underlying graph for the positioning problem. We then perform a thorough evaluation of both possibilities, and compare it with some of the most popular machine learning alternatives. The main conclusion is that these graph-based methods obtain systematically better results, particularly with regards to practical aspects (e.g. gracefully tolerating faulty APs), which makes them a serious candidate to consider when deploying positioning systems.