Publisher Summary This chapter describes iterative methods, mostly based on statistical estimation, which are becoming widely used alternatives to filtered backprojection (FBP). The principal trade-off between iterative techniques and FBP is one of accuracy versus efficiency. Iterative algorithms invariably require repeated calculations of projection and backprojection operations. Thus, they can require substantially greater computation time than FBP. This chapter presents the general principles of iterative image reconstruction and is intended to provide the reader with a starting point for further study. This chapter classifies iterative methods into a few major types and provides details on some prominent examples of these major categories. It is noted that there are many variations on each theme in addition to the examples given. This chapter begins with a formulation of the tomography problem as a linear inverse problem and defines the statistical characteristics of the measured data, then describes the two main components of any iterative method, that is, the criterion for selecting the best image solution and the algorithm for finding that solution.