We review current and emerging knowledge-informed and brain-inspired cognitive systems for realizing adversarial defenses, eXplainable Artificial Intelligence (XAI), and zero-shot or few-shot learning. Data-driven machine learning models have achieved remarkable performance and demonstrated capabilities surpassing humans in many applications. Yet, their inability to exploit domain knowledge leads to serious performance limitations in practical applications. In particular, deep learning systems are exposed to adversarial attacks, which can trick them into making glaringly incorrect decisions. Moreover, complex data-driven models typically lack interpretability or explainability, i.e., their decisions cannot be understood by human subjects. Furthermore, models are usually trained on standard datasets with a closed-world assumption. Hence, they struggle to generalize to unseen cases during inference in practical open-world environments, thus, raising the zero- or few-shot generalization problem. Although many conventional solutions exist, explicit domain knowledge, brain-inspired neural networks and cognitive architectures offer powerful new dimensions towards alleviating these problems. Prior knowledge is represented in appropriate forms like mathematical relations, logic rules, knowledge graphs, and large language models (LLMs). and incorporated in deep learning frameworks to improve performance. Brain-inspired cognition methods use computational models that mimic the human brain to enhance intelligent behavior in artificial agents and autonomous robots. Ultimately, these models achieve better explainability, higher adversarial robustness and data-efficient learning, and can, in turn, provide insights for cognitive science and neuroscience—that is, to deepen human understanding on how the brain works in general, and how it handles these problems.