Deep Learning has enabled machines to learn computational models (i.e., Deep Neural Networks-DNNs) that can perform certain complex tasks with claims to be close to human-level precision. This state-of-the-art performance offered by DNNs in many Artificial Intelligence (AI) applications has paved their way to being used in several safety-critical applications where even a single failure can lead to catastrophic results. Therefore, improving the robustness of these models to hardware-induced faults (such as soft errors, aging, and manufacturing defects) is of significant importance to avoid any disastrous event. Traditional redundancy-based fault mitigation techniques cannot be employed in a wide of applications due to their high overheads, which, when coupled with the compute-intensive nature of DNNs, lead to undesirable resource consumption. In this article, we present an overview of different low-cost fault-mitigation techniques that exploit the intrinsic characteristics of DNNs to limit their overheads. We discuss how each technique can contribute to the overall resilience of a DNN-based system, and how they can be integrated together to offer resilience against multiple diverse hardware-induced reliability threats. Towards the end, we highlight several key future directions that are envisioned to help in achieving highly dependable DL-based systems.