There's no doubt that the popes have been an elderly bunch.
In the past 500 years, though, there has been one exception: Pope Leo X, elected in 1513 at age 37. You might remember him as the one who granted indulgences and subsequently excommunicated Martin Luther for writing the 95 Theses.
Within that same time frame, the oldest was Pope Celement X, elected in 1670 at age 79 after an intense, five-month conclave. He protested his nomination, citing his advanced age, but was overruled by his fellow cardinals and governed as pope for six years.
(Image via Creative Commons)