Dryland landscapes show a variety of vegetation pattern-formation phenomena; banded vegetation on hill slopes and nearly hexagonal patterns of bare-soil gaps in grasslands (“fairy circles”) are two striking examples. Vegetation pattern formation is a population-level mechanism to cope with water stress. It couples to other response mechanisms operating at lower and higher organization levels, such as phenotypic changes at the organism level and biodiversity changes at the community level, and plays a crucial role in understanding ecosystem function. In this talk I will present a platform of mathematical models for dryland ecosystems and use them to study aspects of ecosystem response to climate change and human intervention. I will discuss the mechanisms that destabilize uniform vegetation and lead to periodic vegetation patterns, the variety of extended and localized patterns that can appear along the rainfall gradient, and what unstable ecosystem states can tell us about high-integrity human intervention, that is, intervention that not only achieves its goals but also helps keeping the ecosystem functional in a variable environment.