Understanding the evolution and physical drivers of drought is critical to informing forecasting efforts. One aspect that has seldom been explored is the joint evolution of droughts in space and time. Most studies fix the reference area and focus on their temporal variability, or study their spatial heterogeneity over fixed durations. This work implements a Lagrangian approach by aggregating contiguous areas under drought into clusters. These clusters become the frame of reference and are tracked as they evolve through space and time. Clusters were identified from soil moisture data from the Climate Forecast System Reanalysis (1979-2009). Evapotranspiration, moisture fluxes, and precipitation were used to explore the relevance of possible mechanisms of drought propagation. While most droughts remain near their origin, the centroid of 10% of clusters traveled at least 1,400-3,100 km, depending on the continent. This approach also revealed that large-scale droughts often lock into further growth and intensification.