Hybrid zones are interfaces between populations which can occur when two genetically distinct groups interbreed, but hybrid offspring have a lower evolutionary fitness. We can model this situation using the spatial Lambda-Fleming-Viot process. I will discuss a result on the motion of hybrid zones and also a related probabilistic proof of a well-known PDE result connecting the Allen-Cahn equation and mean curvature flow. Joint work with Alison Etheridge and Nic Freeman.