Edge-cloud collaborative computing (ECCC) has emerged as a pivotal paradigm for addressing the computational demands of modern intelligent applications, integrating cloud resources with edge devices to enable efficient, low-latency processing. Recent advancements in AI, particularly deep learning and large language models (LLMs), have dramatically enhanced the capabilities of these distributed systems, yet introduce significant challenges in model deployment and resource management. In this survey, we comprehensive examine the intersection of distributed intelligence and model optimization within edge-cloud environments, providing a structured tutorial on fundamental architectures, enabling technologies, and emerging applications. Additionally, we systematically analyze model optimization approaches, including compression, adaptation, and neural architecture search, alongside AI-driven resource management strategies that balance performance, energy efficiency, and latency requirements. We further explore critical aspects of privacy protection and security enhancement within ECCC systems and examines practical deployments through diverse applications, spanning autonomous driving, healthcare, and industrial automation. Performance analysis and benchmarking techniques are also thoroughly explored to establish evaluation standards for these complex systems. Furthermore, the review identifies critical research directions including LLMs deployment, 6G integration, neuromorphic computing, and quantum computing, offering a roadmap for addressing persistent challenges in heterogeneity management, real-time processing, and scalability. By bridging theoretical advancements and practical deployments, this survey offers researchers and practitioners a holistic perspective on leveraging AI to optimize distributed computing environments, fostering innovation in next-generation intelligent systems.