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, 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 regard to practical aspects (e.g., gracefully tolerating faulty APs), which makes them a serious candidate to consider when deploying positioning systems.