For the smoker at home, treating anything under a year as rest and anything beyond a year as aging is a useful working line. The industry itself is less tidy. Tobacco may already have years of bale aging before rolling, and finished cigars sit anywhere from weeks to more than a year before release. A cigar arriving in your humidor today may already have several years of pre-roll and post-roll history that the shop has not advertised.
Aging in the deliberate sense is reserved for cigars built to reward five and ten years on a shelf. Padrón 1926 and 1964 Anniversary, the Cohiba Behikes, Davidoff Millennium and Aniversario, Fuente OpusX, certain regional Habanos releases. These are cigars whose makers expect them to deepen over time, and they do.
Cigar Journal and other industry references describe broad aging stages: a green or sick stage in the first one to three years, an aged stage from three to five where flavours continue to develop pleasantly, and a mature stage from six years onward where tannic compounds decompose further and flavours reach what many palates consider their peak. Past fifteen or twenty years, opinion divides.
What does not age well is mild, mass-market, short-filler tobacco. A budget Honduran sandwich cigar will not, after five years on your shelf, become a Padrón 1964. It will be itself with slightly fewer rough edges.
The full argument on which cigars reward long aging is in How to Rest a Cigar.