This paper provides a comprehensive description of the newest version of the Dynamic Global Vegetation Model with managed Land, LPJmL4. This model simulates - internally consistently - the growth and productivity of both natural and agricultural vegetation as coherently linked through their water, carbon, and energy fluxes. These features render LPJmL4 suitable for assessing a broad range of feedbacks within and impacts upon the terrestrial biosphere as increasingly shaped by human activities such as climate change and land use change. Here we describe the core model structure, including recently developed modules now unified in LPJmL4. Thereby, we also review LPJmL model developments and evaluations in the field of permafrost, human and ecological water demand, and improved representation of crop types. We summarize and discuss LPJmL model applications dealing with the impacts of historical and future environmental change on the terrestrial biosphere at regional and global scale and provide a comprehensive overview of LPJmL publications since the first model description in 2007. To demonstrate the main features of the LPJmL4 model, we display reference simulation results for key processes such as the current global distribution of natural and managed ecosystems, their productivities, and associated water fluxes. A thorough evaluation of the model is provided in a companion paper. By making the model source code freely available at https://gitlab.pik-potsdam.de/lpjml/LPJmL we hope to stimulate the application and further development of LPJmL4 across scientific communities in support of major activities such as the IPCC and SDG process.