  Geometric graph is a special kind of graph with geometric features, which is
vital to model many scientific problems. Unlike generic graphs, geometric
graphs often exhibit physical symmetries of translations, rotations, and
reflections, making them ineffectively processed by current Graph Neural
Networks (GNNs). To tackle this issue, researchers proposed a variety of
Geometric Graph Neural Networks equipped with invariant/equivariant properties
to better characterize the geometry and topology of geometric graphs. Given the
current progress in this field, it is imperative to conduct a comprehensive
survey of data structures, models, and applications related to geometric GNNs.
In this paper, based on the necessary but concise mathematical preliminaries,
we provide a unified view of existing models from the geometric message passing
perspective. Additionally, we summarize the applications as well as the related
datasets to facilitate later research for methodology development and
experimental evaluation. We also discuss the challenges and future potential
directions of Geometric GNNs at the end of this survey.
