During natural viewing large saccades shift the visual gaze from one target to another every few hundreds of milliseconds. The role of microsaccades (MSs), small saccades that show up during long fixations, is still debated. A major debate is whether MSs are used to redirect the visual gaze to a new location or to encode visual information through their movement. We argue that these two functions cannot be optimized simultaneously and present several pieces of evidence suggesting that MSs redirect the visual gaze and that the visual details are sampled and encoded by ocular drifts. We show that drift movements are indeed suitable for visual encoding. Yet, it is not clear to what extent drift movements are controlled by the visual system, and to what extent they interact with saccadic movements. We analyze several possible control schemes for saccadic and drift movements and propose experiments that can discriminate between them. We present the results of preliminary analyses of existing data as a sanity check to the testability of our predictions.