Bamboos are perennial woody grasses that display an enigmatic mix of traits. Bamboo is highly shade intolerant like early‐successional trees. Without secondary xylem, bamboos cannot continue to grow once they reach a maximum height or replace xylem damaged by hydraulic stress and must instead replace each stem after a few years using vegetative propagation via rhizomes. These traits of bamboo would appear to make them inferior to trees in competition for both light and water in all but early‐successional wet locations. However, some species competitively exclude trees and form persistent monodominant stands across large areas in tropical and temperate forests, including areas that are not mesic. Moreover, bamboo paradoxically postpones seed production for decades to over a century, and then flowers semelparously and dies synchronously. The delayed reproduction appears to be inconsistent with an early‐successional strategy to colonize disturbed areas as soon as they form, while the simultaneous death over large areas appears to be inconsistent with a late‐successional strategy to gain and hold space. Bamboo exhibits great diversity in its growth form and life histories along the tropical‐temperate geographical cline, with tropical bamboo being taller with shorter rhizome lengths and flowering interval lengths than temperate bamboo. We hypothesize that all of the above characteristics of bamboo are essential elements of competitive strategies to arrest succession in a lineage that lacks secondary xylem. To develop this Arrested Succession Hypothesis, we construct mathematical models of competition for recently disturbed areas between a tree species and a species with bamboo's enigmatic characteristics. We modeled the growth of bamboo genetic individuals from seedlings after seed germination to clonal culms at mass flowering and then placed these individuals in competition with one another and with trees in simple models of competition for light. Results explain how bamboo's traits allow it to persist in forests late in succession despite its hydraulic disadvantages, and form monodominant stands in the temperate zone, but not in tropical forests. They explain why bamboo is semelparous with synchronized reproduction, and why maximum culm size and age, reproductive interval, and rhizome length differ between the tropics and the temperate zone.