Since the mid of 1990s, functional connectivity study using fMRI (fcMRI) has drawn increasing attention of neuroscientists and computer scientists, since it opens a new window to explore functional network of human brain with relatively high resolution. A variety of methods for fcMRI study have been proposed. This paper intends to provide a technical review on computational methodologies developed for fcMRI analysis. From our perspective, these computational methods are classified into two general categories: model-driven methods and data-driven methods. Data-driven methods are a large family, and thus are further sub-classified into decomposition-based methods and clustering analysis methods. For each type of methods, principles, main contributors, and their advantages and drawbacks are discussed. Finally, potential applications of fcMRI are overviewed.