Communities of microorganisms (microbiota) are present in all habitats on Earth and are relevant for agriculture, health, and climate. Deciphering the mechanisms that determine microbiota dynamics and functioning within the context of their respective environments or hosts (the microbiomes) is crucially important. However, the sheer taxonomic, metabolic, functional, and spatial complexity of most microbiomes poses substantial challenges to advancing our knowledge of these mechanisms. While nucleic acid sequencing technologies can chart microbiota composition with high precision, we mostly lack information about the functional roles and interactions of each strain present in a given microbiome. This limits our ability to predict microbiome function in natural habitats and, in the case of dysfunction or dysbiosis, to redirect microbiomes onto stable paths. Here, we will discuss a systematic approach (dubbed the N+1/N-1 concept) to enable step-by-step dissection of microbiome assembly and functioning, as well as intervention procedures to introduce or eliminate one particular microbial strain at a time. The N+1/N-1 concept is informed by natural invasion events and selects culturable, genetically accessible microbes with well-annotated genomes to chart their proliferation or decline within defined synthetic and/or complex natural microbiota. This approach enables harnessing classical microbiological and diversity approaches, as well as omics tools and mathematical modeling to decipher the mechanisms underlying N+1/N-1 microbiota outcomes. Application of this concept further provides stepping stones and benchmarks for microbiome structure and function analyses and more complex microbiome intervention strategies.