Cascading disasters progress from one hazard event to a range of interconnected events and impacts, with often devastating consequences. Rain-related cascading disasters are a particularly frequent form of cascading disasters in many parts of the world, and they are likely to become even more frequent due to climate change and accelerating coastal development, among other issues. (1) Background: The current literature review extended previous reviews of documented progressions from one natural hazard event to another, by focusing on linkages between rain-related natural hazard triggers and infrastructural impacts. (2) Methods: A wide range of case studies were reviewed using a systematic literature review protocol. The review quality was enhanced by only including case studies that detailed mechanisms that have led to infrastructural impacts, and which had been published in high-quality academic journals. (3) Results: A sum of 71 articles, concerning 99 case studies of rain-related disasters, were fully reviewed. Twenty-five distinct mechanisms were identified, as the foundation for a matrix running between five different natural hazards and eight types of infrastructural impacts. (4) Conclusion: Relatively complex quantitative methods are needed to generate locality-specific, cascading disaster likelihoods and scenarios. Appropriate methods can leverage the current matrix to structure both Delphi-based approaches and network analysis using longitudinal data.