<p>Over the last decade, research into the structural and functional organization of the human brain using functional magnetic resonance imaging (fMRI) has shifted its focus from functional segregation, i.e., the functional specialization of individual brain structures, to functional integration, i.e., systems-organized brain activity. Currently, the most common type of fMRI study is resting-state functional connectivity analysis, due to the relative ease of obtaining and statistically processing such data. At the same time, increasing attention is being paid to studies of dynamic changes in functional connectivity during task performance. This review describes the nature of functional connectivity as measured using fMRI, provides a list of existing statistical methods for analysis of task-modulated functional connectivity, and gives practical recommendations for selecting analysis methods and planning the design of fMRI test tasks. In conclusion, we discuss the significance and prospects of research into the modulation of functional connections during the performance of test tasks for fundamental research into the systems-based organization of the human brain in health and pathology.</p>