Network quantization has proven to be a powerful approach to reduce the memory and computational demands of deep learning models for deployment on resource-constrained devices. However, traditional quantization methods often rely on access to training data, which is impractical in many real-world scenarios due to privacy, security, or regulatory constraints. Zero-shot Quantization (ZSQ) emerges as a promising solution, achieving quantization without requiring any real data. In this paper, we provide a comprehensive overview of ZSQ methods and their recent advancements. First, we provide a formal definition of the ZSQ problem and highlight the key challenges. Then, we categorize the existing ZSQ methods into classes based on data generation strategies, and analyze their motivations, core ideas, and key takeaways. Lastly, we suggest future research directions to address the remaining limitations and advance the field of ZSQ. To the best of our knowledge, this paper is the first in-depth survey on ZSQ.