We have a radon mitigation system.

Basically there's a fan that sucks gas from under our foundation and blows it out of our house. They are pretty standard here.

Here is a link that might be useful: Consumer's Guide to Radon Reduction

We put pipes in under the foundation and ran it up to the attic in anticipation of a potential radon problem. So easy to do and inexpensive when the foundation is open that it's a no-brainer. We were glad we did as our radon count upon completion was extremely high. We had a fan put in and now the radon is well below the limit. And as the pipes are in under the foundation, it captures the gas before it ever enters the home.

Energy Vanguard is a blog I read regularly and he has a good post on radon. Basically, best advice is to install during construction. See link below.

Here is a link that might be useful: Energy Vanguard post on radon

A product called "StegoWrap" is the only subfloor poly that prevents the mitigation of radon gas through your concrete slab. THIS is a huge thing, because even with a passive system (pipe under slab with stack through roof), sometimes the easier path for radon is still through your basement slab and into the living space.

Radon causes something like 24% of lung cancer deaths in non-smokers. Which is crazy! The stegowrap is SUPER strong which to me made it WAY superior to regular poly contractors use. Just walking on regular poly creates hundreds of perforations for gas to penetrate (and moisture!). We laid down stego and actually wheeled full wheelbarrows of concrete around on it all morning without a single puncture! On coarse 2" clean limestone.

Then you can also add a small fan to your radon pipe to help draw air out from under the subfloor AND seal up the slab-wall joints with acoustical sealant!

Works wonderfully for my place and I sit right on bedrock.