Video recommender systems are among the most popular and impactful applications of AI, shaping content consumption and influencing culture for billions of users. Traditional single-model recommenders, which optimize static engagement metrics, are increasingly limited in addressing the dynamic requirements of modern platforms. In response, multi-agent architectures are redefining how video recommender systems serve, learn, and adapt to both users and datasets. These agent-based systems coordinate specialized agents responsible for video understanding, reasoning, memory, and feedback, to provide precise, explainable recommendations. In this survey, we trace the evolution of multi-agent video recommendation systems (MAVRS). We combine ideas from multi-agent recommender systems, foundation models, and conversational AI, culminating in the emerging field of large language model (LLM)-powered MAVRS. We present a taxonomy of collaborative patterns and analyze coordination mechanisms across diverse video domains, ranging from short-form clips to educational platforms. We discuss representative frameworks, including early multi-agent reinforcement learning (MARL) systems such as MMRF and recent LLM-driven architectures like MACRec and Agent4Rec, to illustrate these patterns. We also outline open challenges in scalability, multimodal understanding, incentive alignment, and identify research directions such as hybrid reinforcement learning-LLM systems, lifelong personalization and self-improving recommender systems.