Collagens and elastin are 'building blocks' of tissues and extracellular matrix. Mutations in these proteins cause severe congenital syndromes. Adverse genetic variations may accelerate the aging process in adults contributing to premature morbidity, disability and/or mortality. Favorable variants may contribute to longevity and/or healthy aging, but this is much less studied. We reviewed the association between variation in the genes of collagens and elastin and premature aging, accelerated aging, age-related diseases and/or frailty; and the association between genetic variation in those and longevity and/or healthy aging in humans. A systematic search was conducted in MEDLINE and other online databases (OMIM, Genetics Home Reference, Orphanet, ClinVar). Results suggest that genetic variants lead to aging phenotypes of known congenital disease, but also to association with common age-related diseases in adults without known congenital disease. This may be due to the variable penetrance and expressivity of many variants. Some collagen variants have been associated with longevity or healthy aging. A limitation is that most studies had <1000 participants and their criterion for statistical significance was p < 0.05. Results highlight the importance of adopting a lifecourse approach to the study of the genomics of aging. Gerontology can help with new methodologies that operationalize biological aging.