This paper summarizes recent data on the initiation of saccadic eye movement in relation to the mechanisms of visual attention. In particular, the occurrence of express saccades, defined by their extremely short reaction times, is discussed on the basis of the observation that these saccades do not occur when the subjects (man or monkey) are attending to either a fixation point or to any other visual stimulus in the periphery of their field of view including the "future" saccade target location. It is concluded that the system of visual attention can be in two states: engaged or disengaged. In order to generate a saccade or to move attention from one point to another visual attention must be in the disengaged state. The disengagement takes some time which is or is not included in the saccadic reaction time depending on whether or not visual attention is engaged at the time of the onset of the saccade target. During engaged visual attention saccades are inhibited thereby providing steady central fixation or the absence of saccades during directed peripheral attention.