Statistical image reconstruction methods have played an important role in emission computed tomography (ECT) since they accurately model the statistical noise associated with gamma-ray projection data. Although the use of statistical methods in clinical practice in early days was of a difficult problem due to high per-iteration costs and large numbers of iterations, with the development of fast algorithms and dramatically improved speed of computers, it is now inevitably becoming more practical. Some statistical methods are indeed commonly available from nuclear medicine equipment suppliers. In this paper, we first describe a mathematical background for statistical reconstruction methods, which includes assumptions underlying the Poisson statistical model, maximum likelihood and maximum a posteriori approaches, and prior models in the context of a Bayesian framework. We then review a recent progress in developing fast iterative algorithms.