These lenses, sometimes called gas-perm, have been around for many years. They are not the old fashioned "hard" lenses, which was not breathable and could cause long term corneal re-shaping problems. Current gas-permeable lenses are made of very breathable material.
Pros: Very breathable with a lower risk of eye infection compared to soft. Any prescription can be put in a gas-perm lens. Stable vision and long lens life is another plus.
Cons: Some initial discomfort. When starting to wear gas-perm lenses you must maintain and follow your wearing schedule. They are not recommended for full contact sports where soft contact lenses are preferred.
Hybrid lenses: Gas-perm center with a soft lens edge, have been around for a few years. While not for everybody, they have the best of both types of lenses (soft and gas-permeable). Semi-scleral lenses have been here for several years and are ideal for patients with corneal diseases or post-corneal transplant.
A good source for more gas-permeable contact lens information is here at: contactlenses.org