Recommender systems serve as foundational infrastructure in modern information ecosystems, helping users navigate digital content and discover items aligned with their preferences. At their core, recommender systems address a fundamental problem: matching users with items. Over the past decades, the field has experienced successive paradigm shifts, from collaborative filtering and matrix factorization in the machine learning era to neural architectures in the deep learning era. Recently, the emergence of generative models, especially large language models (LLMs) and diffusion models, have sparked a new paradigm: generative recommendation, which reconceptualizes recommendation as a generation task rather than discriminative scoring. This survey provides a comprehensive examination through a unified tripartite framework spanning data, model, and task dimensions. Rather than simply categorizing works, we systematically decompose approaches into operational stages-data augmentation and unification, model alignment and training, task formulation and execution. At the data level, generative models enable knowledge-infused augmentation and agent-based simulation while unifying heterogeneous signals. At the model level, we taxonomize LLM-based methods, large recommendation models, and diffusion approaches, analyzing their alignment mechanisms and innovations. At the task level, we illuminate new capabilities including conversational interaction, explainable reasoning, and personalized content generation. We identify five key advantages: world knowledge integration, natural language understanding, reasoning capabilities, scaling laws, and creative generation. We critically examine challenges in benchmark design, model robustness, and deployment efficiency, while charting a roadmap toward intelligent recommendation assistants that fundamentally reshape human-information interaction.