  Graph neural networks (GNNs) have attracted considerable attention from the
research community. It is well established that GNNs are usually roughly
divided into spatial and spectral methods. Despite that spectral GNNs play an
important role in both graph signal processing and graph representation
learning, existing studies are biased toward spatial approaches, and there is
no comprehensive review on spectral GNNs so far. In this paper, we summarize
the recent development of spectral GNNs, including model, theory, and
application. Specifically, we first discuss the connection between spatial GNNs
and spectral GNNs, which shows that spectral GNNs can capture global
information and have better expressiveness and interpretability. Next, we
categorize existing spectral GNNs according to the spectrum information they
use, \ie, eigenvalues or eigenvectors. In addition, we review major theoretical
results and applications of spectral GNNs, followed by a quantitative
experiment to benchmark some popular spectral GNNs. Finally, we conclude the
paper with some future directions.
