The suits have become the talk of the world swimming championships in Rome, Italy.
The key word in the row is polyurethane. It's the material the newest suits are made from it and helps swimmers go more quickly than ever before.
It works by pushing water away from the swimmer, as well as helping them to stay afloat. It also helps them cut through the water with very little resistance.
Olympic legend Michael Phelps - who won eight golds in Beijing - was beaten the for the first time in four years recently, by someone wearing the most up-to-date outfit.
Michael Phelps' suit only covers the lower half of his body
But that's not to say that Phelps' gear doesn't help him move quickly too, as it also has some polyurethane in it, although there's not as much so it doesn't make as much of a difference. And he only wears the suit on the lower half of his body.
The people who run swimming - world swimming governing body Fina - are going to bring in new rules next year to say how much of the athletes body can be covered and what their swimsuits can be made of.
They say they want to get back to a sport where fans are talking about the swimmers' talent in the water and not the suits they're wearing.