The proliferation of false information in the digital age has become a pressing concern, necessitating the development of effective and robust detection methods. This paper offers a comprehensive review of existing false information detection techniques, approached from a novel perspective that emphasizes the propagation characteristics of misinformation. We introduce a new taxonomy that categorizes these methods into homogeneous and heterogeneous propagation-based approaches, providing a deeper understanding of the varying scopes and complexities involved in information dissemination. For each category, we present a formal problem formulation, review commonly used datasets, and summarize state-of-the-art methods. Additionally, we identify several promising directions for future research, including the creation of a unified benchmark suite, exploration of diverse information modalities, and development of innovative rumor debunking tasks. By systematically organizing the vast array of current techniques, this work offers a clear overview of the research landscape, aiding researchers and practitioners in navigating this complex field and inspiring further advancements.