Cognitive neuroscience of the healthy aging human brain has thus far addressed age-related changes of local functional and structural properties of gray and white matter and their association with declining or preserved cognitive functions. In addition to these localized changes, recent neuroimaging research has attributed an important role to neural networks with a stronger focus on interacting rather than isolated brain regions. The analysis of functional connectivity encompasses task-dependent and -independent synchronous activity in the brain, and thus reflects the organization of the brain in distinct performance-relevant networks. Structural connectivity in white matter pathways, representing the integrity of anatomical connections, underlies the communication between the nodes of these functional networks. Both functional and structural connectivity within these networks have been demonstrated to change with aging, and to have different predictive values for cognitive abilities in older compared to young adults. Structural degeneration has been found in the entire cerebral white matter with greatest deterioration in frontal areas, affecting whole brain structural network efficiency. With regard to functional connectivity, both higher and lower functional coupling has been observed in the aging compared to the young brain. Here, high connectivity within the nodes of specific functional networks on the one hand, and low connectivity to regions outside this network on the other hand, were associated with preserved cognitive functions in aging in most cases. For example, in the language domain, connections between left-hemisphere language-related prefrontal, posterior temporal and parietal areas were described as beneficial, whereas connections between the left and right hemisphere were detrimental for language task performance. Of note, interactions between structural and functional network properties may change in the course of aging and differentially impact behavioral performance in older versus young adults. Finally, studies using noninvasive brain stimulation techniques like transcranial direct current stimulation (tDCS) to simultaneously modulate behavior and functional connectivity support the importance of 'selective connectivity' of aging brain networks for preserved cognitive functions. These studies demonstrate that enhancing task performance by tDCS is paralleled by increased connectivity within functional networks. In this review, we outline the network perspective on healthy brain aging and discuss recent developments in this field.