Droughts spread through interrelated land-atmosphere systems and hydrological processes, and evolve into different types of droughts, such as hydrological, agricultural, ecological, and socioeconomic droughts, in different geographical and temporal contexts. Against the backdrop of global climate change and intensified human activities, the propagation and evolution of different types of drought present more uncertainties. Over the past decade, our understanding of the spatiotemporal characteristics, research methods, evolutionary processes, and driving factors of drought propagation has gradually deepened, but clear scientific views have not been realized. Beginning from the definition of drought propagation, this study systematically analyzed the scientific connotation of the problem and clarified the developmental stages of drought propagation research. Six quantitative research methods for current drought propagation were comprehensively summarized: threshold method and run theory, correlation analysis, causal analysis, cross-wavelet analysis, probability models, and meteorological-hydrological models. Furthermore, from the perspective of meteorological-hydrological and meteorological-agricultural drought propagation scenarios and drought propagation driving forces, the main acquired scientific knowledge was analyzed and summarized. The findings reveal the propagation order, stage threshold, spatiotemporal heterogeneity, and human-driven processes of drought propagation research worldwide. Finally, a series of challenges that future drought propagation research will face were analyzed. These include further exploration of spatiotemporal heterogeneity in the propagation process, bridging the gap between mathematical and physical knowledge to establish trustworthy models, and integrating cross-disciplinary knowledge to achieve a full-process analysis of propagation. The systematical analysis of the progress and challenges of domestic and international drought propagation research will provide key theoretical and methodological support for the next steps in drought disaster analysis and scientific management.