Soft technology has been an emerging field since flexible and wearable electronics started flourishing. In this research field, oxides can play an important role due to their intriguing functionalities and superior thermal and chemical stabilities. To deliver high-quality thin films or structures based on oxides, heteroepitaxy is essential. However, the lack of a suitable approach remains an obstacle for flexible oxide heteroepitaxy. Recently, due to the advancement of growth facilities and characterization tools, various techniques have been employed to acquire flexible oxide heteroepitaxy. This review highlights the methods as well as direct and indirect approaches that are essential for developing oxide heteroepitaxy with mechanical flexibility. We also provide an overview, classifying the fields in terms of applications involving flexible oxide heteroepitaxy and the development of oxide-based approaches.