Modern deep neural networks (DNNs) are achieving state-of-the-art results due to their capability to learn a faithful representation of the data they are trained on. In this chapter, we address two insufficiencies of DNNs, namely, the lack of robustness to corruptions in the data, and the lack of real-time deployment capabilities, that need to be addressed to enable their safe and efficient deployment in real-time environments. We introduce hybrid corruption-robustness focused compression (HCRC), an approach that jointly optimizes a neural network for achieving network compression along with improvement in corruption robustness, such as noise and blurring artifacts that are commonly observed. For this study, we primarily consider the task of semantic segmentation for automated driving and focus on the interactions between robustness and compression of the network. HCRC improves the robustness of the DeepLabv3+ network by 8.39% absolute mean performance under corruption (mPC) on the Cityscapes dataset, and by 2.93% absolute mPC on the Sim KI-A dataset, while generalizing even to augmentations not seen by the network in the training process. This is achieved with only minor degradations on undisturbed data. Our approach is evaluated over two strong compression ratios (30% and 50%) and consistently outperforms all considered baseline approaches. Additionally, we perform extensive ablation studies to further leverage and extend existing state-of-the-art methods.