In upright stance, individuals sway continuously and the sway pattern in dual tasks (e.g., a cognitive task performed in upright stance) differs significantly from that observed during the control quiet stance task. The cognitive approach has generated models (limited attentional resources, U-shaped nonlinear interaction) to explain such patterns based on competitive sharing of attentional resources. The objective of the current manuscript was to review these cognitive models in the specific context of visual tasks involving gaze shifts toward precise targets (here called active vision tasks). The selection excluded the effects of early and late stages of life or disease, external perturbations, active vision tasks requiring head and body motions and the combination of two tasks performed together (e.g., a visual task in addition to a computation in one's head). The selection included studies performed by healthy, young adults with control and active - difficult - vision tasks. Over 174 studies found in Pubmed and Mendeley databases, nine were selected. In these studies, young adults exhibited significantly lower amplitude of body displacement (center of pressure and/or body marker) under active vision tasks than under the control task. Furthermore, the more difficult the active vision tasks were, the better the postural control was. This underscores that postural control during active vision tasks may rely on synergistic relations between the postural and visual systems rather than on competitive or dual relations. In contrast, in the control task, there would not be any synergistic or competitive relations.