The concept of interhemispheric competition has been very influential in attention research, and the occurrence of biased attention due to an imbalance in posterior parietal cortex (PPC) is well documented. In this context, the vast majority of studies have assessed attentional performance with tasks that did not include an explicit experimental manipulation of attention, and, as a consequence, it remains largely unknown how these findings relate to core attentional constructs such as endogenous and exogenous control and spatial orienting and reorienting. We here addressed this open question by creating an imbalance between left and right PPC with transcranial direct current stimulation, resulting in right-hemispheric dominance, and assessed performance on three experimental paradigms that isolate distinct attentional processes. The comparison between active and sham transcranial direct current stimulations revealed a highly informative pattern of results with differential effects across tasks. Our results demonstrate the functional necessity of PPC for endogenous and exogenous attentional control and, importantly, link the concept of interhemispheric competition to core attentional processes, thus moving beyond the notion of biased attention after noninvasive brain stimulation over PPC.