Cross-modality visible-infrared person reidentification (VI-ReID) has attracted widespread concern due to its scalability in 24-h video surveillance of the Visual Internet of Things (VIoT). Driven by enough annotated training data, supervised VI-ReID has achieved superior performance. However, annotating a large amount of cross-modality data is extremely time-consuming, which limits its employment in real-world scenarios. Existing several works neglect the image-level discrepancy and could not obtain reliable feature-level heterogeneous correlation. In this article, we propose a novel homogeneous and heterogeneous optimization with modality style adaptation (HHO) mechanism to eliminate intramodality and intermodality discrepancies without any label information for unsupervised VI-ReID. Specifically, we present the modality style adaptation strategy to transfer unlabeled cross-modality pedestrian styles, which not only increases the image diversity but also bridges the intermodality gap. Meanwhile, we employ the clustering algorithm to generate pseudo labels for each modality. The homogeneous feature optimization is developed to extract intramodality pedestrian features. Furthermore, we propose heterogeneous feature optimization to eliminate the intermodality discrepancy. To this end, a heterogeneous feature search (HFS) module is designed to mine reliable cross-modality signals for each identity. These reliable heterogeneous features are constrained to generate the compact feature distribution, while different identities are forced to be separated. The HHO are seamlessly integrated to learn cross-modality robust features. Abundant experiments prove the superiority of HHO, which gains superior performance.