While the last few decades have witnessed a huge body of work devoted to inference and learning in distributed and decentralized setups, much of this work assumes a non-adversarial setting in which individual nodes---apart from occasional statistical failures---operate as intended within the algorithmic framework. In recent years, however, cybersecurity threats from malicious non-state actors and rogue entities have forced practitioners and researchers to rethink the robustness of distributed and decentralized algorithms against adversarial attacks. As a result, we now have a plethora of algorithmic approaches that guarantee robustness of distributed and/or decentralized inference and learning under different adversarial threat models. Driven in part by the world's growing appetite for data-driven decision making, however, securing of distributed/decentralized frameworks for inference and learning against adversarial threats remains a rapidly evolving research area. In this article, we provide an overview of some of the most recent developments in this area under the threat model of Byzantine attacks.