Here we critically review studies that used electroencephalography (EEG) or event-related potential (ERP) indices as a biomarker of Alzheimer's disease. In the first part we overview studies that relied on visual inspection of EEG traces and spectral characteristics of EEG. Second, we survey analysis methods motivated by dynamical systems theory (DST) as well as more recent network connectivity approaches. In the third part we review studies of sleep. Next, we compare the utility of early and late ERP components in dementia research. In the section on mismatch negativity (MMN) studies we summarize their results and limitations and outline the emerging field of computational neurology. In the following we overview the use of EEG in the differential diagnosis of the most common neurocognitive disorders. Finally, we provide a summary of the state of the field and conclude that several promising EEG/ERP indices of synaptic neurotransmission are worth considering as potential biomarkers. Furthermore, we highlight some practical issues and discuss future challenges as well.