Aim: To understand the geographical distribution of grasses in sub-Saharan Africa with reference to key plant traits thought to affect range size in this family (Poaceae). Specifically, to test hypotheses on the importance of plant height and lifespan in determining range size and invasion potential in the context of their evolutionary history. > Location: Sub-Saharan Africa. Taxon: Poaceae. Methods: The range sizes of 757 grass species native to southern Africa were estimated for the sub-Saharan African region from geo-referenced herbarium records using the alpha hull function. Phylogenetic generalised least squares models and linear mixed effects models were fitted to test whether grass range size was related to plant height and lifespan. Tribe-level relationships between range size and plant height were assessed with linear models. For species introduced to other continents, generalised linear mixed effects models were fitted to test whether invasiveness was related to native range size, plant height and lifespan. Differences in native range size among species in four invasion-related categories were assessed with linear mixed effects models. Results: Grass range sizes are larger for taller species and for species with shorter lifespans. The relationship between plant height and range size varies widely among tribes, with some range-restricted tribes having a non-significant effect on plant height. Grasses with larger native range sizes and shorter lifespans are more likely to become invasive after being introduced to other continents. Grass species introduced to other continents have larger native range sizes than those that have not, and native range size increases along the introduced-naturalised-invasive continuum. Main conclusions: The increased dispersal opportunities of annual-biannual grasses appear to have a greater positive effect on range size than do the longer generation times of perennial grasses. Grass height has and continues to be an important driver of grass biogeography, with implications for understanding the spread of certain grass tribes over the Miocene. Factors that promote large native range sizes are also likely to increase the probability of a species becoming invasive. Keywords: alpha hull, biogeography, distribution, extent of occurrence (EOO), invasive, phylogeny, Poaceae, range size.