Driven by massive amounts of web-scale data, generative AI (GenAI) has achieved remarkable progress, enabling various applications in diverse sectors. The advances of GenAI have actuated practitioners to use AI-synthesized data for training next-generation AI models. Undeniably, using synthetic data has alleviated the increasing stringent demand for data supply. Unfortunately, it also introduces a new critical issue: in a self-consuming cycle between model and data, the model ultimately collapse, raising more trustworthiness concerns to GenAI. In recent years, increasingly more studies have investigated the phenomenon of model collapse (MC) and explored potential solutions to mitigate it. However, the review of the phenomenon of MC still remains blank. To fill this gap, this paper provides an up-to-date overview of these studies for consolidating and reviewing the progress of MC in different application scenarios and countermeasures for mitigating MC. We also highlight challenges and future research opportunities.