Magnesium (Mg) and its alloys, known for their low density and high specific strength, are increasingly explored as lightweight structural materials across a broad range of industrial applications. However, their widespread application remains constrained by intrinsic mechanical limitations, fundamentally rooted in the nature of crystallographic defects. Atomic-scale modeling techniques are transforming our ability to unravel the structures, energetics, and dynamics of these defects and to explore their complex interactions, thereby guiding defect engineering in Mg alloys. However, the growing body of available data can make it difficult for researchers to identify critical knowledge gaps and promising areas for further exploration. To address this challenge, we highlight key research domains with significant potential for impactful advancements, aiming to illuminate these areas while inspiring innovative approaches and encouraging deeper exploration of pivotal topics that may shape the future of Mg alloy development. This review presents a comprehensive overview of the state-of-the-art in atomic-scale modeling of defects in Mg and its alloys. We introduce key simulation methodologies, including density functional theory and atomistic simulations, and highlight their applications to defect distribution, defect dynamics, and defect-defect interactions. By bridging fundamental insights in defects with alloy design strategies, this review aims to support and inspire the broader Mg research community and to underscore the growing impact of atomic-scale modeling in the accelerated development of high-performance Mg alloys.