The human gut microbiota is engaged in multiple interactions affecting host health during the host's entire life span. Microbes colonize the neonatal gut immediately following birth. The establishment and interactive development of this early gut microbiota are believed to be (at least partially) driven and modulated by specific compounds present in human milk. It has been shown that certain genomes of infant gut commensals, in particular those of bifidobacterial species, are genetically adapted to utilize specific glycans of this human secretory fluid, thus representing a very intriguing example of host-microbe coevolution, where both partners are believed to benefit. In recent years, various metagenomic studies have tried to dissect the composition and functionality of the infant gut microbiome and to explore the distribution across the different ecological niches of the infant gut biogeography of the corresponding microbial consortia, including those corresponding to bacteria and viruses, in healthy and ill subjects. Such analyses have linked certain features of the microbiota/microbiome, such as reduced diversity or aberrant composition, to intestinal illnesses in infants or disease states that are manifested at later stages of life, including asthma, inflammatory bowel disease, and metabolic disorders. Thus, a growing number of studies have reported on how the early human gut microbiota composition/development may affect risk factors related to adult health conditions. This concept has fueled the development of strategies to shape the infant microbiota composition based on various functional food products. In this review, we describe the infant microbiota, the mechanisms that drive its establishment and composition, and how microbial consortia may be molded by natural or artificial interventions. Finally, we discuss the relevance of key microbial players of the infant gut microbiota, in particular bifidobacteria, with respect to their role in health and disease.