  Recent years have witnessed fast developments of graph neural networks (GNNs)
that have benefited myriads of graph analytic tasks and applications. In
general, most GNNs depend on the homophily assumption that nodes belonging to
the same class are more likely to be connected. However, as a ubiquitous graph
property in numerous real-world scenarios, heterophily, i.e., nodes with
different labels tend to be linked, significantly limits the performance of
tailor-made homophilic GNNs. Hence, GNNs for heterophilic graphs are gaining
increasing research attention to enhance graph learning with heterophily. In
this paper, we provide a comprehensive review of GNNs for heterophilic graphs.
Specifically, we propose a systematic taxonomy that essentially governs
existing heterophilic GNN models, along with a general summary and detailed
analysis. Furthermore, we discuss the correlation between graph heterophily and
various graph research domains, aiming to facilitate the development of more
effective GNNs across a spectrum of practical applications and learning tasks
in the graph research community. In the end, we point out the potential
directions to advance and stimulate more future research and applications on
heterophilic graph learning with GNNs.
