The process of refinement is such a large problem in function minimization that even the computers of today cannot perform the calculations to properly fit X-ray diffraction data. Each of the refinement packages currently under development reduces the difficulty of this problem by utilizing a unique combination of targets, assumptions and optimization methods. This review summarizes the basic methods and underlying assumptions in the commonly used refinement packages. This information can guide the selection of a refinement package that is best suited for a particular refinement project.