For an elementary particle to possess a permanent electric dipole moment (EDM), time-reversal symmetry must be violated. This implies the violation of CP symmetry. The known CP violation in the standard model generates very small EDMs, but many extensions to the standard model introduce new sources of CP violation which give rise to EDMs near the current experimental limits. For example, CP violation in supersymmetric models is already strongly constrained by the need to keep the predicted values of EDMs small. Most models of baryogensis also require new sources of CP violation to give a matter dominated universe. We have made the most precise measurement of the electron EDM by measuring how the spin-precession rate of YbF molecules changes in an applied electric field. The polar molecule enhances the sensitivity to the EDM. I will describe the experiment and our result, and outline our plan to increase the spin precession time by cooling the YbF molecules to ultracold temperatures and then launching them into a fountain.