Maybe underboob sweat absorbers have existed for forever. Maybe your aunt swears by them. Beats me, I don't really know much about boobs besides they're fun to look at, I can't wait to touch some, and apparently they play an important role when you have a baby (I think babies sleep on them?). This is the Belly Bandit Don't Sweat It Comfortable Underbust Sweat Soaker. It costs $20 and soaks up underbreast sweat so it doesn't soak through your shirt. Personally, I always thought underboob sweat was sexy. Unless it causes uncomfortable chafing or poses a drowning risk during motorboating. I swear, women take such good care of themselves and I can't even manage to keep my penis from smelling like a dirty gym sock.
Thanks to Fifi, who just inspired me to always run with a tampon in my navel so I don't get the dreaded belly button sweat ring.