The concept of compliant substrate epitaxy was first proposed by the scientists engaged in crystal growth in the early 1990s. The core idea is to take advantage of such an ultra-thin substrate that the film and the substrate generate strain together to relieve the lattice mismatch during the epitaxy growth. The quality of the epitaxial film is improved due to the reduction of the mismatch dislocation density. However, the preparation of the artificial ultra-thin substrate with good quality requires rather complicated fabrication process. On the other hand, many transition metal dichalcogenides naturally form the compliant substrates, due to their layered structure and weak van der Waals interlayer interaction. In this paper, we introduce the transition metal dichalcogenides based compliant substrate epitaxy model and relevant applications. Through combining density functional theory, linear elasticity theory and dislocation theory, we introduce the model comprehensively by using the Au-MoS2 as a prototypical example. And we explain the experimental results of Au growing on MoS2 from the early transition electron microscopy. In addition, we introduce the experimental work related to the model, especially the Au-mediated exfoliation of large, monolayer and high-quality MoS2. Future directions and relevant important problems to be solved are also discussed.