LSMs are critical pieces of Earth system models, needed for the projection of the extent of global change, as well as impacts on critical terrestrial systems such as agriculture, freshwater resources, ecosystems, and built infrastructure. However, LSM predictions show a stubborn uncertainty that has been difficult to attribute to specific process representations and parameter values.  At the same time, the scope of LSMs has grown complex—for valid reasons—because of the many interacting processes that make up terrestrial systems. We argue that, as a first “Grand Challenge,” the LSM community must focus more clearly on the process complexity of LSMs, in order to better allow scaling from simplified models to the highly interacting representation of a full LSM.  A second “Grand Challenge” relates to the differing views of heterogeneity in LSMs, which focus on various subsets and combinations of, e.g., disturbance, hillslopes, microclimate, vegetation communities, recent weather, snow depth, land management, and others.  But a general approach to identifying what are the dominant dimensions of heterogeneity at a given location, and how to most efficiently resolve that heterogeneity has not yet emerged.  A third “Grand Challenge” is on how to understand the dynamics of model parameters that are governed by complex interactions between physical and ecological dynamics; in particular, we review three leading approaches: empirical, optimality-based, and competition-resolving, and identify questions about when to use each of these, how different aspects may and may not be combined, and what the implications are for each of these.