Although infantilism is mostly what I know, this talk is going to be about ageplay in general; I'll speak as broadly as I can.
One word about those involuntary emotional "alarm bells." In our society we're virtually trained to react with at least discomfort whenever anybody mentions the words "sex" and "children" in the same sentence. But when I talk about "children" I will mean not actual children, but adults who are roleplaying in a consensual, negotiated scene.
Or, they may want to live a childhood they never had.
One can roleplay a child or teen of the opposite sex, or from a different time period (the old-time schoolhouse, or being a child in the Roman Empire), or even a scenario that's totally made up (being a teenager in a world in which it's perfectly acceptable for parents to punish unruly teens with, say, bondage).
For one thing, how many of us can remember our childhoods exactly?
There are a few elements commonly seen in ageplay: clothes and costumes are one, from little frilly baby dresses, footed PJs and snap-crotch Oshkosh overalls to school uniforms and whatever wacky fashions are popular among those crazy kids today.
Other "props" can play a part, from pacifiers, toys, crayons, fingerpaint and even elaborate baby furniture to sports equipment, skateboards, blow dryers and curling irons for those older kids.
Sometimes, for example, the roles ageplayers fantasize about playing are based on the way children live today, rather than the way they lived when they themselves were growing up.
Children nowadays have more money of their own and wear more expensive clothes than they did even 20 years ago.