Neurological and psychiatric disorders have often an underlying structural components, such as alterations of synaptic function, degeneration of connectivity and cell death, etc. In addition they lead to a wide spectrum of cognitive impairments, affecting multiple domains and which are often shared between pathologies with very different physiopathology. Remarkably, the level of cognitive impairments can be very diverse across different subjects and patients with similar level of pathology-induced circuit alterations. Such resilience of certain individuals to the deleterious effects of physiopathological processes has been interpreted in terms of the elusive concept of "cognitive reserve", whose activity- and network-level correlates remain poorly characterized. Here, moving from general theoretical considerations and computational modelling predictions, we speculate that the capacity of brain networks to maintain a spatio-temporally complex and fluidly reconfiguring collective dynamics underlies the maintenance of cognitive performance, despite structural degradations. We provide then experimental evidence corroborating (even if not yet fully proving) this hypothesis considering analyses of LFP and spikes, EEG and fMRI recordings in human patients and mouse models of disorders as epilepsy and Alzheimer's disease. Our theory open the way to the design of future interventional approaches which would aim at "refueling/boosting cognitive reserve", by restoring a healthy brain dynamics on top of still degenerating brain structures.