Lateralized, non-informative visual cues lengthen reaction time (RT) to successive targets flashed in the same hemified. Early ipsilateral RT facilitation is limited to the co-occurrence of cues and targets. Inhibition from visual cues has sensory components which do not depend on orienting, as well as attentional components which are limited to one side of the vertical meridian. An inhibition of RT to targets ipsilateral to the cues has been found with somatic or auditory cues and targets, and also when somatic targets follow visual cues or visual targets follow somatic cues. The results reviewed in this paper (1) are best accounted for by directional constraints in motor readiness which are induced by the voluntary suppression of an overt orienting toward the location of the cue; (2) indicate that similar mechanisms of covert orienting operate in the whole peripersonal and near extrapersonal space; and (3) point to a common neural substrate mediating both intramodal and cross-modal effects.