Large Language Models (LLMs) deliver powerful AI capabilities but face deployment challenges due to high resource costs and latency, whereas Small Language Models (SLMs) offer efficiency and deployability at the cost of reduced performance. Collaboration between LLMs and SLMs emerges as a crucial paradigm to synergistically balance these trade-offs, enabling advanced AI applications, especially on resource-constrained edge devices. This survey provides a comprehensive overview of LLM-SLM collaboration, detailing various interaction mechanisms (pipeline, routing, auxiliary, distillation, fusion), key enabling technologies, and diverse application scenarios driven by on-device needs like low latency, privacy, personalization, and offline operation. While highlighting the significant potential for creating more efficient, adaptable, and accessible AI, we also discuss persistent challenges including system overhead, inter-model consistency, robust task allocation, evaluation complexity, and security/privacy concerns. Future directions point towards more intelligent adaptive frameworks, deeper model fusion, and expansion into multimodal and embodied AI, positioning LLM-SLM collaboration as a key driver for the next generation of practical and ubiquitous artificial intelligence.