Microbiomes are complex and ubiquitous networks of microorganisms whose seemingly limitless chemical transformations could be harnessed to benefit agriculture, medicine, and biotechnology. The spatial and temporal changes in microbiome composition and function are influenced by a multitude of molecular and ecological factors. This complexity yields both versatility and challenges in designing synthetic microbiomes and perturbing natural microbiomes in controlled, predictable ways. In this review, we describe factors that give rise to emergent spatial and temporal microbiome properties and the meta-omics and computational modeling tools that can be used to understand microbiomes at the cellular and system levels. We also describe strategies for designing and engineering microbiomes to enhance or build novel functions. Throughout the review,we discuss key knowledge and technology gaps for elucidating the networks and deciphering key control points for microbiome engineering, and highlight examples where multiple omics and modeling approaches can be integrated to address these gaps. Expected final online publication date for the Annual Review of Biomedical Engineering, Volume 23 is June 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.