Land surface models (LSMs) are a vital tool for understanding, projecting, and predicting the dynamics of the land surface and its role within the Earth system, under global change. Driven by the need to address a set of key questions, LSMs have grown in complexity from simplified representations of land surface biophysics to encompass a broad set of interrelated processes spanning the disciplines of biophysics, biogeochemistry, hydrology, ecosystem ecology, community ecology, human management, and societal impacts. This vast scope and complexity, while warranted by the problems LSMs are designed to solve, has led to enormous challenges in understanding and attributing differences between LSM predictions. Meanwhile, the wide range of spatial scales that govern land surface heterogeneity, and the broad spectrum of timescales in land surface dynamics, create challenges in tractably representing processes in LSMs. We identify three "grand challenges" in the development and use of LSMs, based around these issues: managing process complexity, representing land surface heterogeneity, and understanding parametric dynamics across the broad set of problems asked of LSMs in a changing world. In this review, we discuss progress that has been made, as well as promising directions forward, for each of these challenges.Plain Language Summary Land surface models (LSMs) are the part of climate models that simulate processes happening at the Earth's surface. These include reflection of the sunlight, evaporation from ecosystems, and the amount of carbon from human emissions that the land takes up. LSMs also need to simulate how human management of the land surface changes the climate both directly (e.g., via the effect on evaporation) and in the long term (via changing the amount of carbon stored in wood and soil). Not surprisingly, trying to make a single mathematical representation of all of these different parts of the Earth system is difficult. Here we discuss themes that repeatedly affect all teams developing LSMs: how to manage the increasing number of complicated model components, how to represent the high degree of variability of the land surface, and how to predict how the properties of the surface (particularly those of plant communities) will change. These are large problems, with no obvious easy solutions. We hope to spark discussion and investment into their resolution, concomitant with the increasing importance of LSMs as our best tools for translating possible trajectories of climate change into impacts on humans, ecosystems, food and water supplies, and river systems.