Alzheimer’s disease (AD) is a degenerative brain disease with a high and irreversibleincidence. In recent years, because brain signals have complex nonlinear dynamics, there has beengrowing interest in studying complex changes in the time series of brain signals in patients withAD. We reviewed studies of complexity analyses of single-channel time series fromelectroencephalogram (EEG), magnetoencephalogram (MEG), and functional magnetic resonanceimaging (fMRI) in AD and determined future research directions. A systematic literature search for2000–2019 was performed in the Web of Science and PubMed databases, resulting in 126 identifiedstudies. Compared to healthy individuals, the signals from AD patients have less complexity andmore predictable oscillations, which are found mainly in the left parietal, occipital, right frontal, andtemporal regions. This complexity is considered a potential biomarker for accurately responding tothe functional lesion in AD. The current review helps to reveal the patterns of dysfunction in thebrains of patients with AD and to investigate whether signal complexity can be used as a biomarkerto accurately respond to the functional lesion in AD. We proposed further studies in the signalcomplexities of AD patients, including investigating the reliability of complexity algorithms and thespatial patterns of signal complexity. In conclusion, the current review helps to better understandthe complexity of abnormalities in the AD brain and provide useful information for AD diagnosis.