Approximate Nearest Neighbor Search (ANNS) underpins many large-scale data mining and machine learning applications, with efficient retrieval increasingly hinging on GPU acceleration as dataset sizes grow. Although graph-based approaches represent the state of the art in approximate nearest neighbor search, there is a lack of systematic understanding regarding their optimization for modern GPU architectures and their end-to-end effectiveness in practical scenarios. In this work, we present a comprehensive survey and experimental study of GPU-accelerated graph-based vector search algorithms. We establish a detailed taxonomy of GPU optimization strategies and clarify the mapping between algorithmic tasks and hardware execution units within GPUs. Through a thorough evaluation of six leading algorithms on eight large-scale benchmark datasets, we assess both graph index construction and query search performance. Our analysis reveals that distance computation remains the primary computational bottleneck, while data transfer between the host CPU and GPU emerges as the dominant factor influencing real-world latency at large scale. We also highlight key trade-offs in scalability and memory usage across different system designs. Our findings offer clear guidelines for designing scalable and robust GPU-powered approximate nearest neighbor search systems, and provide a comprehensive benchmark for the knowledge discovery and data mining community.