The propagation of electron spin polarization is receiving increasing attention, for both practical and fundamental reasons. In an electron gas, one might imagine that spin and charge would move at more or less at the same rate, since each electron carries both properties. However, in this talk I will describe experiments that show that this is not the case, even for the weakly interacting electrons in GaAs-based quantum wells. I will emphasize the role of electron-electron and spin-orbit interactions in creating distinct dynamics for the propagation of spin and charge.