This chapter illustrates fundamental concepts, the core research problem, and the contributions of the thesis. It presents the thesis methodologial unified framework of Computer Aided Geometric Design (CAGD) and Deep Learning (DL) and address geometric data approximation problem. Subsequenlty, to resolve the core challenges of data parameterization and approximant design, Truncated Hierarchical B-splines (THB-splines) are introduced together with Convolutional Neural Network (CNN) and Graph Convolutional neural Network (GCN) architectures. Finally, an overview of the novel contributions developed in the following chapters is provided: robust adaptive fitting via reweighted least squares and quasi-interpolation, data-driven parameterization, and the establishment of the moving parameterization paradigm.