In this chapter, we describe the role of attention in the control of smooth pursuit eye movements. As a voluntary and continuous eye movement, smooth pursuit is driven by both visual and cognitive signals. Here we show that whereas the entire process of smooth pursuit requires visual attention, the post-onset phase of the initiation and the maintenance smooth pursuit are under an additional sustained non-visual cognitive attention control. The temporal dynamics of these complementary controls of visual and non-visual cognitive attention support the continuous generation of smooth pursuit so that eye tracking of a moving target can be prompt and accurate.