The intestinal microbiome changes with age, but the causes and consequences of microbiome aging remain unclear. Furthermore, the gut microbiome has been proposed to mediate the benefit of lifespan-extending interventions such as dietary restriction, but this hypothesis warrants further exploration. Here, by analyzing 2997 metagenomes collected longitudinally from 913 deeply phenotyped, genetically diverse mice, we provide new insights into the interplay between the microbiome, aging, dietary restriction, host genetics, and a wide range of health parameters. First, we find that microbiome uniqueness increases with age across datasets and species. Moreover, age-associated changes are better explained by cumulative exposure to stochastic events (neutral theory) than by the influence of an aging host (selection theory). Second, we unexpectedly find that the majority of microbiome features are significantly heritable and that the amount of variation explained by host genetics is as large as that of aging and dietary restriction. Third, we find that the intensity of dietary restriction parallels the extent of microbiome changes and that dietary restriction does not rejuvenate the microbiome. Lastly, we find that the microbiome is significantly associated with multiple health parameters - including body composition, immune parameters, and frailty - but not with lifespan. In summary, this large and multifaceted study sheds light on the factors influencing the microbiome and aspects of host physiology modulated by the microbiome.