Accurate simulation of water’s wave propagation and nonlinear wave transformations is of fundamental importance to marine and coastal engineering. Over the last few decades, significant efforts have been made to develop or improve depth averaged models, and their numerical solutions in order to provide means of accurately predicting near-shore wave processes. This work presents my scientific contributions to numerical schemes for depth-averaged modes, and beyond, over the last ten years. These contributions can be divided into three main categories. First, the study of depth-averaged models where we consider, examine, and compare different families of Boussinsq-type (BT) models. Secondly, the design and implementation of numerical schemes for BT models, where we present a two-step solution procedure that can be applied to a large family of weakly nonlinear BT models. Lastly, we highlight my contributions on wave breaking and the applications of BT models.