Semiarid grasslands have crossed thresholds to shrub-dominated states due to heavy grazing episodes and their after-effects. Extreme weather events and restoration actions can catalyze varying degrees of grass recovery. While we understand these thresholds in biophysical terms, we have scarcely explored their ultimate societal causes. I will reconstruct thought processes underpinning historical desertification events on the Jornada Experimental Range, including some recent first-hand experiences. I also describe how such “mental models” underpin restoration success. Given the large management extents and heterogeneity inherent to drylands, I argue that appropriate mental models are the most important tools we have to manage thresholds.