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It is time-consuming and laborious to manually label a large number of samples, and samples from some rare classes are difficult to obtain. Therefore, the zero-shot image classification has become a research hotspot in the computer vision field. Firstly, the zero-shot learning, including direct push zero-shot learning and inductive zero-shot learning, is introduced briefly. Secondly, the space embedding zero-shot image classification methods and the generative model based zero-shot image classification methods with their subclass methods are introduced emphatically. Meanwhile, the mechanism, advantages and disadvantages, and application scenarios of these methods are analyzed and summarized. Thirdly, the main datasets and main evaluation criteria for zero-shot image classification are briefly introduced, and the performance of typical zero-shot image classification methods is compared. Then, the problems such as domain drift, hubness and semantic gap and the corresponding solutions are pointed out. Finally, the future development trends and research hotspots of zero-shot image classification are discussed, such as the accurate location of discriminative region, visual features of high-quality unseen class, generalized zero-shot image classification, etc.