The appearance of an object in the visual field triggers a shift of gaze toward its location. This orienting response consists of a rapid rotation of the eyes, the saccade, which can be accompanied by a rotation of the head. If the target moves, the saccade is followed by a slow movement of the eyes and a catch-up saccade. In this chapter, instead of describing the path leading from the target-evoked retinal activity to the changes in muscle tension, we shall take the reverse path. Starting from the muscle contractions, we shall proceed upstream and describe the tremendous organization that, in the brainstem and cerebellum, enables us to rapidly and accurately orient the foveae towards visual targets located at different eccentricities and depths. This chapter is an attempt to synthesize the considerable knowledge that neurophysiologists and neuroanatomists gathered in the monkey during the last six decades.