Complex communities of microbes act collectively to regulate human health, provide sources of clean energy, and ripen aromatic cheese. The efficient functioning of these communities can be directly related to competitive and cooperative interactions between species. Physical constraints and local environment affect the stability of these interactions. Here we explore the role of spatial habitat and interaction networks in microbial ecology and human disease. In the first part of the dissertation, we model mutualism to understand how spatial microbial communities survive number fluctuations in physical habitats. We explicitly account for the production, consumption, and diffusion of public goods in a two-species microbial community. We show that increased sharing of nutrients breaks down coexistence, and that species may benefit from making slower-diffusing nutrients. In multi-species communities, indirect and higher order interactions may affect community function. We find that the requirement for spatial proximity severely restricts the network of possible microbial interactions. While cooperation between two species is stable, higher-order mutualism requiring three or more species succumbs easily to number fluctuations. Additional cyclic or reciprocal interactions between pairs can stabilize multi-species communities. Inter-species interactions also affect human health via the human microbiome: microbial communities in the gut, lungs and skin. In the second part of the dissertation, we use machine learning and statistics to establish links between microbiota abundance and composition, and the incidence of chronic diseases. We study the gut fungal profile to probe the effects of diet and fungal dysbiosis in a cohort of Saudi children with Crohn's disease. While statistical microbiome studies established that each disease phenotype is associated with a distinct state of intestinal dysbiosis, they often produced conflicting results and identified a very large number of microbes associated with disease. We show that a handful of taxa could drive the dynamics of ecosystem-level abundance changes due to strong inter-species interactions. Using maximum entropy methods, we propose a simple statistical approach (Direct Association Analysis or DAA) to account for interspecific interactions. When applied to the largest dataset on IBD, DAA detects a small subset of associations directly linked to the disease, avoids p-value inflation and identifies most predictive features of the microbiome.

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