Geometric deep learning extends deep learning to non-Euclidean data structures like graphs and manifolds. Traditional deep learning excels on Euclidean data, such as images, but struggles with data like social networks, sensor networks, or brain imaging, which have non-Euclidean structures. This paper reviews geometric deep learning, focusing on methods to generalize convolutional neural networks (CNNs) to non-Euclidean domains. It discusses challenges, applications, and future directions in this emerging field. The paper begins by explaining the success of CNNs in Euclidean domains, leveraging statistical properties like stationarity and compositionality. It then introduces the concept of non-Euclidean data, which lacks properties like shift-invariance and global parameterization. To address this, geometric deep learning generalizes CNNs using spectral methods, where convolutions are defined in the spectral domain, and spatial methods, where convolutions are defined on the graph or manifold. The paper outlines two main classes of geometric learning problems: structure learning (understanding the domain's structure) and function learning (analyzing functions on the domain). It discusses manifold learning techniques, such as multidimensional scaling and Laplacian eigenmaps, and graph-based methods for analyzing signals on graphs. The paper also covers the mathematical foundations of geometric deep learning, including differential geometry concepts like manifolds, tangent spaces, and Riemannian metrics, as well as graph theory concepts like graph Laplacians and eigenvectors. It explains how these concepts are used to define operations like convolution on non-Euclidean domains. The paper reviews various geometric deep learning paradigms, emphasizing the differences between Euclidean and non-Euclidean learning methods. It discusses spectral methods, which use the eigenvalues and eigenvectors of the Laplacian to define convolutions, and spatial methods, which use local structures on the graph or manifold. It also explores the combination of these approaches using spatio-frequency analysis techniques. The paper provides examples of applications in network analysis, particle physics, recommender systems, computer vision, and graphics. It concludes with a discussion of current challenges and future research directions in geometric deep learning, emphasizing the need for standardized terminology and notation to advance the field.Geometric deep learning extends deep learning to non-Euclidean data structures like graphs and manifolds. Traditional deep learning excels on Euclidean data, such as images, but struggles with data like social networks, sensor networks, or brain imaging, which have non-Euclidean structures. This paper reviews geometric deep learning, focusing on methods to generalize convolutional neural networks (CNNs) to non-Euclidean domains. It discusses challenges, applications, and future directions in this emerging field. The paper begins by explaining the success of CNNs in Euclidean domains, leveraging statistical properties like stationarity and compositionality. It then introduces the concept of non-Euclidean data, which lacks properties like shift-invariance and global parameterization. To address this, geometric deep learning generalizes CNNs using spectral methods, where convolutions are defined in the spectral domain, and spatial methods, where convolutions are defined on the graph or manifold. The paper outlines two main classes of geometric learning problems: structure learning (understanding the domain's structure) and function learning (analyzing functions on the domain). It discusses manifold learning techniques, such as multidimensional scaling and Laplacian eigenmaps, and graph-based methods for analyzing signals on graphs. The paper also covers the mathematical foundations of geometric deep learning, including differential geometry concepts like manifolds, tangent spaces, and Riemannian metrics, as well as graph theory concepts like graph Laplacians and eigenvectors. It explains how these concepts are used to define operations like convolution on non-Euclidean domains. The paper reviews various geometric deep learning paradigms, emphasizing the differences between Euclidean and non-Euclidean learning methods. It discusses spectral methods, which use the eigenvalues and eigenvectors of the Laplacian to define convolutions, and spatial methods, which use local structures on the graph or manifold. It also explores the combination of these approaches using spatio-frequency analysis techniques. The paper provides examples of applications in network analysis, particle physics, recommender systems, computer vision, and graphics. It concludes with a discussion of current challenges and future research directions in geometric deep learning, emphasizing the need for standardized terminology and notation to advance the field.