Interactions between brain regions have been recognized as a critical ingredient required to understand brain function. Two modes of interactions have held prominence—synchronization and causal influence. Efforts to ascertain causal influence from functional magnetic resonance imaging (fMRI) data have relied primarily on confirmatory model-driven approaches, such as dynamic causal modeling and structural equation modeling, and exploratory data-driven approaches such as Granger causality analysis. A slew of recent articles have focused on the relative merits and caveats of these approaches. The relevant studies can be classified into simulations, theoretical developments, and experimental results. In the first part of this review, we will consider each of these themes and critically evaluate their arguments, with regard to Granger causality analysis. Specifically, we argue that simulations are bounded by the assumptions and simplifications made by the simulator, and hence must be regarded only as a guide to experimental design and should not be viewed as the final word. On the theoretical front, we reason that each of the improvements to existing, yet disparate, methods brings them closer to each other with the hope of eventually leading to a unified framework specifically designed for fMRI. We then review latest experimental results that demonstrate the utility and validity of Granger causality analysis under certain experimental conditions. In the second part, we will consider current issues in causal connectivity analysis—hemodynamic variability, sampling, instantaneous versus causal relationship, and task versus resting states. We highlight some of our own work regarding these issues showing the effect of hemodynamic variability and sampling on Granger causality. Further, we discuss recent techniques such as the cubature Kalman filtering, which can perform blind deconvolution of the hemodynamic response robustly well, and hence enabling wider application of Granger causality analysis. Finally, we discuss our previous work on the less-appreciated interactions between instantaneous and causal relationships and the utility and interpretation of Granger causality results obtained from task versus resting state (e.g., ability of causal relationships to provide a mode of connectivity between regions that are instantaneously dissociated in resting state). We conclude by discussing future directions in this area.