What are expansive soils?
Expansive soils (or swelling soils) are clay minerals which have a high capacity for water absorption. As more water is introduced, voids in these clay mineral soils will expand. Conversely, these soils contract as they dry out - leaving large voids in the soils. 
How are clay soils determined to be 'expansive'?
Swelling clays can have a profound impact on any and all other soils even in a small concentration (~5% clay). A potentially expansive clay can be determined to be expansive if lab testing proves that it has a liquid limit around or exceeding 50%, a plasticity index around or exceeding 30%, and/or by measuring the volume change of the clay when immersed in water.
How can damage from expansive soils be prevented or mitigated?
The absolute best way to prevent damage from swelling soils is to extend the foundation of a structure beyond the depth at which water content in the soils will regularly be fluctuating. More recent studies have shown that these depths often extend further than was previously thought. Most areas have a regular wet season and dry season which is easily accounted for, but in the case of a drought followed by an extended wet season, these zones may extend in depth and experience greater differences between their dry volume and wet volume.
What are potential issues caused by expansive soils?
The most apparent and most damaging effect of expansive soils is the 'heaving' of a foundation. Pictures below show just how damaging these soils can be to foundations and walls of homes, as well as retaining walls which are holding soils in place. Piping (especially plastics/PVC) not buried beneath expansive soils is subject to stress and likely to break as it is lifted and compressed by expansive soils. It is worth noting that if water/sewage pipes break they will leak into the soil and exacerbate the swelling of these soils, possibly causing further issues. Concrete drainage piping and drainage ditches are also subject to very similar issues. Cracking will leak water run-off into expansive soils and the vicious cycle of heaving, cracking, and leaking continues.