Depression is a disorder characterized not only by persistent negative mood, lack of motivation and a "ruminative" style of thinking, but also by specific deficits in cognitive functioning. These deficits are especially pronounced when integration of information is required. Previous research on linear syllogisms points to a clear pattern of cognitive disturbances present in people suffering from depressive disorders, as well as in people with elevated negative mood. Such disturbances are characterized by deficits in the integration of piecemeal information into coherent mental representations. In this review, I present evidence which suggests that the dysfunction of specific brain areas plays a crucial role in creating reasoning and information integration problems among people with depression and with heightened negative mood. As the increasingly prevalent systems neuroscience approach is spreading into the study of mental disorders, it is important to understand how and which brain networks are involved in creating certain symptoms of depression. Two large brain networks are of particular interest when considering depression: the default mode network (DMN) and the fronto-parietal (executive) network (FNP). The DMN network shows abnormally high activity in the depressed population, whereas FNP circuit activity is diminished. Disturbances within the FNP network seem to be strongly associated with cognitive problems in depression, especially those concerning executive functions. The dysfunctions within the fronto-parietal network are most probably connected to ineffective transmission of information between prefrontal and parietal regions, and also to an imbalance between FNP and DMN circuits. Inefficiency of this crucial circuits functioning may be a more general mechanism leading to problems with flexible cognition and executive functions, and could be the cause of more typical symptoms of depression like persistent rumination.