The application of transfer learning, an approach utilizing knowledge from a source domain to enhance model performance in a target domain, has seen a tremendous rise in recent years, underpinning many real-world scenarios. The key to its success lies in the shared common knowledge between the domains, a prerequisite in most transfer learning methodologies. These methods typically presuppose identical feature spaces and label spaces in both domains, known as homogeneous transfer learning, which, however, is not always a practical assumption. Oftentimes, the source and target domains vary in feature spaces, data distributions, and label spaces, making it challenging or costly to secure source domain data with identical feature and label spaces as the target domain. Arbitrary elimination of these differences is not always feasible or optimal. Thus, heterogeneous transfer learning, acknowledging and dealing with such disparities, has emerged as a promising approach for a variety of tasks. Despite the existence of a survey in 2017 on this topic, the fast-paced advances post-2017 necessitate an updated, in-depth review. We therefore present a comprehensive survey of recent developments in heterogeneous transfer learning methods, offering a systematic guide for future research. Our paper reviews methodologies for diverse learning scenarios, discusses the limitations of current studies, and covers various application contexts, including Natural Language Processing, Computer Vision, Multimodality, and Biomedicine, to foster a deeper understanding and spur future research.

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