Alzheimer's Disease (AD) is a neurodegenerative disorder and the most common type of dementia with a great prevalence in western countries. The diagnosis of AD and its progression is performed through a variety of clinical procedures including neuropsychological and physical examination, Electroencephalographic (EEG) recording, brain imaging and blood analysis. During the last decades, analysis of the electrophysiological dynamics in AD patients has gained great research interest, as an alternative and cost-effective approach. This paper summarizes recent publications focusing on (a) AD detection and (b) the correlation of quantitative EEG features with AD progression, as it is estimated by Mini Mental State Examination (MMSE) score. A total of 49 experimental studies published from 2009 until 2020, which apply machine learning algorithms on resting state EEG recordings from AD patients, are reviewed. Results of each experimental study are presented and compared. The majority of the studies focus on AD detection incorporating Support Vector Machines, while deep learning techniques have not yet been applied on large EEG datasets. Promising conclusions for future studies are presented.