There is a lot of discussion about crawl space air polluting the air inside your home. Some claims say up to 50% of the air in your home is "dirty" crawl space air. While for certain there is some air transfer between your crawl space and your home, the 50% claim is exaggerated and doesn't account for insulation, flooring, and other barriers that are in between your crawl space and your living spaces above.
This claim is mostly based on something called the stack effect. Everyone understands that hot air rises and cool air falls. The stack effect is most often associated with how draft works in a chimney but also can be applied to how air moves through your home. In the winter, warm air rises first to your second floor and then is lost through leaks in the roof and ceiling insulation, this change in pressure pulls air through your home to escape at the roof. In the summer the process is reversed as cooled air from the HVAC system seeks to "fall" as a result pushes warm air upward. This is why upstairs bedrooms are hotter than lower levels in the summer. In both seasons, this change in air pressure pulls air from the lowest point, your crawl space, so there is some air transfer but a claim of 50% is drastic.
If your crawl space is musty smelling, dirty and moldy and you are experiencing the same musty odor or seeing health related issues with mold or asthma inside your home then certainly your crawl space might be one place to start addressing this problem.