Graph convolutional networks (GCNs) showed promising results in learning from point cloud data. Applications of GCNs include point cloud classification, point cloud segmentation, point cloud upsampling, and more. Recently, the introduction of Deep Graph Convolutional Networks (DeepGCNs) allowed GCNs to go deeper, and thus resulted in better graph learning while avoiding the vanishing gradient problem in GCNs. By adapting impactful methods from convolutional neural networks (CNNs) such as residual connections, dense connections, and dilated convolutions, DeepGCNs allowed GCNs to learn better from non-Euclidean data. In addition, deep learning methods proved very effective in the task of point cloud upsampling. Unlike traditional optimization-based methods, deep learning-based methods to point cloud upsampling does not rely on priors nor hand-crafted features to learn how to upsample point clouds. In this thesis, I discuss the impact and show the performance results of DeepGCNs in the task of point cloud part segmentation on PartNet dataset. I also illustrate the significance of using GCNs as upsampling modules in the task of point cloud upsampling by introducing two novel upsampling modules: Multi-branch GCN and Clone GCN. I show quantitatively and qualitatively the performance results of our novel and versatile upsampling modules when evaluated on a new proposed standardized dataset: PU600, which is the largest and most diverse point cloud upsampling dataset currently in the literature.