Large-scale pre-trained Vision Language Models (VLMs) have proven effective for zero-shot classification. Despite the success, most traditional VLMs-based methods are restricted by the assumption of partial source supervision or ideal target vocabularies, which rarely satisfy the open-world scenario. In this paper, we aim at a more challenging setting, Realistic Zero-Shot Classification, which assumes no annotation but instead a broad vocabulary. To address the new problem, we propose the Self Structural Semantic Alignment (S3A) framework, which extracts the structural semantic information from unlabeled data while simultaneously selflearning. Our S3A framework adopts a unique Cluster-Vote-Prompt-Realign (CVPR) algorithm, which iteratively groups unlabeled data to derive structural semantics for pseudo-supervision. Our CVPR algorithm includes iterative clustering on images, voting within each cluster to identify initial class candidates from the vocabulary, generating discriminative prompts with large language models to discern confusing candidates, and realigning images and the vocabulary as structural semantic alignment. Finally, we propose to self-train the CLIP image encoder with both individual and structural semantic alignment through a teacher-student learning strategy. Our comprehensive experiments across various generic and fine-grained benchmarks demonstrate that the S3A method substantially improves over existing VLMs-based approaches, achieving a more than 15% accuracy improvement over CLIP on average. Our codes, models, and prompts are publicly released at https://github.com/shengeatamath/S3A.