The Matrix model uses transition matrices to predict future plant and animal population structures. Having been used to study the dynamics of forests all over the world, the Matrix model is thriving in forestry, with applications covering a wide array of areas. Despite its extensive
application in forestry, the Matrix model is still suffering from a lack of due attention and appropriate understanding, especially on its advantages and limitations in comparison with those of other forest dynamics models. To facilitate further research and applications, a synthetic review
of Matrix models is provided here with an emphasis on its mathematical properties and relationship with other forest dynamics models. In this article, we first introduce the general structure of Matrix models and its representation of forest dynamics components, i.e., upgrowth, mortality,
and recruitment. Then, we summarize key properties of Matrix models, including basic assumptions, density dependence, size class width and time step, and the estimation of forest dynamics components will be summarized. Next, we evaluate advantages and limitations of the Matrix model and its
relationship with other forest dynamics models. Finally, we share our perspective on the major challenges and future outlooks of Matrix models.