Zero-shot learning is gaining increasing attention in the social computing community, primarily because it can enable models to effectively perform classification or regression tasks when new concepts continually emerge while lacking sufficient training samples in certain categories. Zero-shot image classification, as a concrete application of zero-shot learning, requires the model to classify images into unknown categories without seeing any training samples of those categories. The key issue of zero-shot image classification is how to leverage auxiliary information such as attributes and textual descriptions to establish connections between the visual space and the semantic space. With the advancement of deep learning theories and methods, the way of modeling cross-modal interaction has continuously improved, promoting significant progress in zero-shot image classification. In this survey, we intensively review related literature in the field of zero-shot image classification over the past decade, with specific elaborations on the latest progress under three scenarios: Traditional zero-shot learning, generalized zero-shot learning, and compositional zero-shot learning. Besides, challenges that need to be addressed as well as prospects of emerging techniques like large language models in zero-shot image classification are also discussed.