Graph neural networks have emerged in the past years as very promising methods for the analysis of graph-structured data. Useful insights can in fact be extracted by allowing learning models to take into account relationships between entities in a graph. The main methods used in the context of graph neural networks are here described and compared, with a focus on the extension of convolutional layers to graph structures. Afterwards, an analysis of how attention mechanisms integrate with graph neural networks is introduced. In this context a new method is proposed for allowing a graph neural network to attend over its own input in the context of graph classification.