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This review provides a comprehensive overview of the state-of-the-art methods of graphbased networks from a deep learning perspective. Graph networks provide a generalized form to exploit non-euclidean space data. A graph can be visualized as an aggregation of nodes and edges without having any order. Data-driven architecture tends to follow a fixed neural network trying to find the pattern in feature space. These strategies have successfully been applied to many applications for euclidean space data. Since graph data in a non-euclidean space does not follow any kind of order, these solutions can be applied to exploit the node relationships. Graph Neural Networks (GNNs) solve this problem by exploiting the relationships among graph data. Recent developments in computational hardware and optimization allow graph networks possible to learn the complex graph relationships. Graph networks are therefore being actively used to solve many problems including protein interface, classification, and learning representations of fingerprints. To encapsulate the importance of graph models, in this paper, we formulate a systematic categorization of GNN models according to their applications from theory to real-life problems and provide a direction of the future scope for the applications of graph models as well as highlight the limitations of existing graph networks.INDEX TERMS Graph neural network, geometric deep learning, graph-structured network, non-euclidean space.