In this paper, we study a setting in which two terminals A and B respectively observe, or measure, noisy versions X̃ and Ỹ of two memoryless, possibly statistically dependent, remote sources X and Y; and they interact bidirectionally in the aim of computing functions of the remote sources. Focusing on a distributed source coding formulation, we establish characterizations of the rate-distortion region and the minimum sum-rate for any finite number of messages. This generalizes Ma and Ishwar's two-terminal function computation result to the case of remote sources. Furthermore, in the case in which the computation is performed at only one side, we establish upper bounds on the maximum gain that can be brought up by the interaction in terms of the minimum sum rate improvement for a given average distortion. We also apply the results to some important special cases, thus allowing us to gain some fundamental insights on the benefits of the interaction for both lossless and lossy function computations in these cases.