Since ancient Greek times, we've known that we smell differently when we are unwell. While we rely on blood analysis today, ancient Greek physicians used smell to diagnose maladies. If they took a whiff of your breath and described it as fetor hepaticus (meaning bad liver), it meant you could be headed for liver failure.
If a person's whiff was sweet or fruity, physicians thought this meant that sugars in the digestive system were not being broken down, and that person probably had diabetes. Science has since shown the ancient Greeks were right – liver failure and diabetes and many other diseases including infectious diseases give your breath a distinctive smell.