Brain lesions to the white matter in peritrigonal regions, periventricular leukomalacia, in children who were born prematurely represent an important model for studying limitations on brain development. The lesional pattern is of early origin and bilateral, that constrains the compensatory potential of the brain. We suggest that (i) topography and severity of periventricular lesions may have a long-term predictive value for cognitive and social capabilities in preterm birth survivors; and (ii) periventricular lesions may impact cognitive and social functions by affecting brain connectivity, and thereby, the dissociable neural networks underpinning these functions. A further pathway to explore is the relationship between cerebral palsy and cognitive outcome. Restrictions caused by motor disability may affect active exploration of surrounding and social participation that may in turn differentially impinge on cognitive development and social cognition. As an outline for future research, we underscore sex differences, as the sex of a preterm newborn may shape the mechanisms by which the developing brain is affected.