The recent wave of impressive results obtained in fields as varied as computer vision, natural language processing, bioinformatics and many more can be attributed to the advances in training and designing neural networks. A neural network works as a universal function approximator, so that it can use training data to learn complex input-output mappings. This chapter presents spectral approaches to the definition of graph-convolutional layers, drawing from literature on the graph Fourier transform (GFT). It focuses on the spatial definitions of graph convolution, which have emerged as a more flexible alternative, providing superior experimental performance. The spectral approach to graph convolution is desirable as it is mathematically principled, relying on the spectral domain induced by the GFT. The graph convolution network has been applied in numerous applications and it is one of the most well-known graph convolutional neural networks. Computational complexity is a major issue, especially for adaptive approaches deriving weights as functions of features.