Recently, AI-driven interactions with computing devices have advanced from basic prototype tools to sophisticated, LLM-based systems that emulate human-like operations in graphical user interfaces. We are now witnessing the emergence of \emph{Computer-Using Agents} (CUAs), capable of autonomously performing tasks such as navigating desktop applications, web pages, and mobile apps. However, as these agents grow in capability, they also introduce novel safety and security risks. Vulnerabilities in LLM-driven reasoning, with the added complexity of integrating multiple software components and multimodal inputs, further complicate the security landscape. In this paper, we present a systematization of knowledge on the safety and security threats of CUAs. We conduct a comprehensive literature review and distill our findings along four research objectives: \textit{\textbf{(i)}} define the CUA that suits safety analysis; \textit{\textbf{(ii)} } categorize current safety threats among CUAs; \textit{\textbf{(iii)}} propose a comprehensive taxonomy of existing defensive strategies; \textit{\textbf{(iv)}} summarize prevailing benchmarks, datasets, and evaluation metrics used to assess the safety and performance of CUAs. Building on these insights, our work provides future researchers with a structured foundation for exploring unexplored vulnerabilities and offers practitioners actionable guidance in designing and deploying secure Computer-Using Agents.