Cognitive reserve and resilience refer to the set of processes allowing the preservation of cognitive performance in the presence of structural and functional brain changes. Investigations of these concepts have provided unique insights into the heterogeneity of cognitive and brain changes associated with aging. Previous work mainly relied on methods benefiting from a high spatial precision but a low temporal resolution, and thus the temporal brain dynamics underlying these concepts remains poorly known. Moreover, while spontaneous fluctuations of neural activity have long been considered as noise, recent work highlights its critical contribution to brain functions. In this study, we synthesized the current state of knowledge from magnetoencephalography (MEG) and electroencephalography (EEG) studies that investigated the contribution of maintenance of neural synchrony, and variability of brain dynamics, to cognitive changes associated with healthy aging and the progression of neurodegenerative disease (such as Alzheimer's disease). The reviewed findings highlight that compensations could be associated with increased synchrony of higher (>10 Hz) frequency bands. Maintenance of young-like synchrony patterns was also observed in healthy older individuals. Both maintenance and compensation appear to be highly related to preserved structural integrity (brain reserve). However, increased synchrony was also found to be deleterious in some cases and reflects neurodegenerative processes. These results provide major elements on the stability or variability of functional networks as well as maintenance of neural synchrony over time, and their association with individual cognitive changes with aging. These findings could provide new and interesting considerations about cognitive reserve, maintenance, and resilience of brain functions and cognition.