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Atmospheric boundary-layer dynamics over heterogeneous surfaces is significant to a wide array of geophysical and engineering applications. Yet, despite over five decades of intense efforts by the research community, numerous open research questions remain. This underlines the complexity of the physical processes that are excited by heterogeneity, the multitude of patterns and manifestations that it can display, and the importance of the implications to research in the atmospheric sciences and beyond. Here, existing knowledge is reviewed and a path forward for research is proposed, starting with the smaller scales near a surface transition and proceeding to the influence on large-scale dynamics and their forecasting.