The human brain contains an intricate network of about 100 billion neurons. Aging of the brain is characterized by a combination of synaptic pruning, loss of cortico-cortical connections, and neuronal apoptosis that provoke an age-dependent decline of cognitive functions. Neural/synaptic redundancy and plastic remodeling of brain networking, also secondary to mental and physical training, promote maintenance of brain activity and cognitive status in healthy elderly subjects for everyday life. However, age is the main risk factor for neurodegenerative disorders such as Alzheimer's disease (AD) that impact on cognition. Growing evidence supports the idea that AD targets specific and functionally connected neuronal networks and that oscillatory electromagnetic brain activity might be a hallmark of the disease. In this line, digital electroencephalography (EEG) allows noninvasive analysis of cortical neuronal synchronization, as revealed by resting state brain rhythms. This review provides an overview of the studies on resting state eyes-closed EEG rhythms recorded in amnesic mild cognitive impairment (MCI) and AD subjects. Several studies support the idea that spectral markers of these EEG rhythms, such as power density, spectral coherence, and other quantitative features, differ among normal elderly, MCI, and AD subjects, at least at group level. Regarding the classification of these subjects at individual level, the most previous studies showed a moderate accuracy (70-80%) in the classification of EEG markers relative to normal and AD subjects. In conclusion, resting state EEG makers are promising for large-scale, low-cost, fully noninvasive screening of elderly subjects at risk of AD.