Aging is a major risk factor for many types of cancer, and the molecular mechanisms implicated in aging, progeria syndromes, and cancer pathogenesis display considerable similarities. Maintaining redox homeostasis, efficient signal transduction, and mitochondrial metabolism is essential for genome integrity and for preventing progression to cellular senescence or tumorigenesis. NAD+ is a central signaling molecule involved in these and other cellular processes implicated in age-related diseases and cancer. Growing evidence implicates NAD+ decline as a major feature of accelerated aging progeria syndromes and normal aging. Administration of NAD+ precursors such as nicotinamide riboside (NR) and nicotinamide mononucleotide (NMN) offer promising therapeutic strategies to improve health, progeria comorbidities, and cancer therapies. This review summarizes insights from the study of aging and progeria syndromes and discusses the implications and therapeutic potential of the underlying molecular mechanisms involved in aging and how they may contribute to tumorigenesis.