The advance of deep learning has shown great potential in applications (speech, image, and video classification). In these applications, deep learning models are trained by datasets in Euclidean space with fixed dimensions and sequences. Nonetheless, the rapidly increasing demands on analyzing datasets in non-Euclidean space require additional research. Generally speaking, finding the relationships of elements in datasets and representing such relationships as weighted graphs consisting of vertices and edges is a viable way of analyzing datasets in non-Euclidean space. However, analyzing the weighted graph-based dataset is a challenging problem in existing deep learning models. To address this issue, graph neural networks (GNNs) leverage spectral and spatial strategies to extend and implement convolution operations in non-Euclidean space. Based on graph theory, a number of enhanced GNNs are proposed to deal with non-Euclidean datasets. In this study, we first review the artificial neural networks and GNNs. We then present ways to extend deep learning models to deal with datasets in non-Euclidean space and introduce the GNN-based approaches based on spectral and spatial strategies. Furthermore, we discuss some typical Internet of Things (IoT) applications that employ spectral and spatial convolution strategies, followed by the limitations of GNNs in the current stage.