Also called chronophilia (and sometimes ageism), the fetishization of age is a hotly debated topic in gay culture. The term swings both ways: this fetish applies when someone older fetishizes the specific the specific age of someone younger and when someone younger fetishizes the specific age of someone older. The fetish doesn't require a significant age difference - just the fact that someone's age itself is a turn-on.
Conceptually, this fetish opens up debate surrounding the fetishization of other characteristics like skin color and body type. Some argure that fetishizing certain physical characteristics like age and weight is no different than feet and hand fetishes, which we generally do not frown upon. Others say that age fetishes, like skin color and body type fetishes, are not fetishes at all and the reduction of a person's features into points of desire (and, by extension, rejection) is dehumanizing and smacks of racism and body-shaming.
Debate rages. Age fetish deserves inclusion on this for the sheer purpose that it shows how fetishes can cross from the playfully erotic into more culturally profound and impactful subjects. The whole concept of fetish reveals that anything in the world, from pool floats to ice cream, can become sexual objects if someone responds to them that way and as such they unleash our secual deisres from the narrow confines that our culture tends to place them them in.