The rapid development of Artificial Intelligence (AI), and especially Agentic AI, is reshaping how work is organized at both the individual and organizational levels. An emerging organizational form—the One-Person Agentic Company (OPAC)—allows a solo or a few founders to orchestrate specialized agent swarms to manage complex business functions through real-time analysis and adaptive coordination. Unlike the traditional one-person company, which offers strong individual control but limited scalability, OPAC extends one-person productivity by combining human leadership with a multi-agent workforce powered by large language models and multimodal models. Despite growing interest, OPAC has emerged as an important research direction, yet the field remains in its early stages. Existing research is fragmented across AI foundation, multi-agent systems, human–computer interaction, and management. This survey provides the first systematic review of research relevant to OPACs. We define OPAC through four organizational characteristics from both technical and management perspectives. We further compare OPACs with traditional companies in terms of organizational composition, cost structure, efficiency, development logic, authority, and risk. We then organize the literature into four thematic areas critical to the technical and managerial design of OPAC. Specifically, we review how OPACs are structured and operate, how agent-related resources are allocated and governed, how such organizations develop through agent and workflow updates, and how reliability, accountability, and human control can be maintained amid increasing agentic delegation. By connecting advances in LLM-based agents and multi-agent systems with management research on organizational design, resource allocation, adaptation, and governance, this survey clarifies the current research landscape of OPACs, highlights critical open challenges, and outlines future directions for scalable and trustworthy human-led agentic enterprises.