Distinct biological species can coexist in the same ecosystem by occupying distinct niches. However, the niches available in a given environment -- which reflect the range of environmental conditions and limiting factors that are present -- are not necessarily a fixed property of the system. Environmental conditions can be shaped, and possibly diversified, by the resident community, through modifications that range from chemical excretion to physical remodeling to biotic control of local environmental microbiomes. To varying degrees, all species modify their local environment, driving changes that can feed back to affect the set of available niches and ultimately the composition and coexistence of the community. Here, we study minimal mathematical models for these kinds of modifications in the context of community coexistence. We review some existing empirical and theoretical approaches to understanding environmental feedbacks, highlighting the essential similarities in the dynamics of several system-specific examples. We then extend and carefully examine one prominent model for plant-soil feedbacks, a broad class of environmental feedbacks that operate in plant communities. We show that this widely-used model cannot account for the coexistence of more than two plant species. We go on to develop a simple, nested modeling framework for environmental feedbacks based on the classic metapopulation paradigm. We show that this model can account for the coexistence of an arbitrary number of species, and we derive analytical characterizations of when and how species coexist in ecosystems with environmental feedbacks.