A number of studies have shown that the microbial communities of the human body are integral for the maintenance of human health. Advances in next-generation sequencing have enabled rapid and large-scale quantification of the composition of microbial communities in health and disease. Microorganisms mediate diverse host responses including metabolic pathways and immune responses. Using a system biology approach to further understand the underlying alterations of the microbiota in physiological and pathological states can help reveal potential novel therapeutic and diagnostic interventions within the field of synthetic biology. Tools such as biosensors, memory arrays, and engineered bacteria can rewire the microbiome environment. In this article, we review the computational tools used to study microbiome communities and the current limitations of these methods. We evaluate how genome-scale metabolic models (GEMs) can advance our understanding of the microbe-microbe and microbe-host interactions. Moreover, we present how synergies between these system biology approaches and synthetic biology can be harnessed in human microbiome studies to improve future therapeutics and diagnostics and highlight important knowledge gaps for future research in these rapidly evolving fields.