Abstract: Grasslands cover 25% of the earth’s surface and are important as a feed source for livestock, as habitat for wildlife, and as a provider of environmental services. Woody plant encroachment threatens grasslands globally, and simulation modeling is used increasingly as a decision support tool to address this threat. We reviewed simulation models dealing with woody plant encroachment published during the past decade with the goal of identifying the types and locations of the grasslands modeled, characterizing the types of models used, and summarizing model results and challenges for future modeling efforts. We based our search on the Web of Science (2013-2022). Our search query and relevance criteria yielded a total of 31 publications, cited 689 times (679 without self-citations). Four of the 31 publications were reviews. The top ten words used in the body of the 31 texts were model (n=1153), vegetation (n=979), soil (n=957), grass (n=923), trees (n=797), plant (n=782), water (n=672), change (n=671), and shrub (n=651). The frequent usage of the words ‘soil’ and ‘water’ exemplifies the importance of these two factors in modeling woody encroachment, as well as the incorporation of an ecohydrology perspective. The authors of most of the publications were affiliated with the United States (14) and Germany (12) (we limited our search to articles published in English). From our preliminary results, we found that systems modeled varied widely, including areas in Argentina, China, Ethiopia, Italy, Namibia, South Africa, Spain, and the United States. The spatial scales modeled varied as well, ranging from small pastures to a global extent. Grand challenges to modeling woody plant encroachment included representation of the effects of climate change, land degradation, and other anthropogenic pressures, particularly those affecting ecohydrology.