The exponential radial profiles of spiral galaxies have been observed for decades with various explanations offered, but none of these explanations hold up now that the profiles have been traced to 10 scale lengths in some cases. Profiles with breaks also have their outer parts remarkably close to exponential. This is true in both spirals and dwarfs, with a particular problem for non-barred dwarfs where there are no strong torques or shears in the stellar disks for radial scattering. We have shown that scattering from disk clumps can make exponentials, and indeed dwarfs have fairly massive clumps and irregularities in their HI distributions. Spiral waves also have clumps in the form of persistent wave enhancements at corotation and at points of wave interference. This talk reviews the observations of exponential profiles and profile breaks in spiral and dwarf galaxies, and considers various theories to explain them.