This paper reviews recent progress in the diagnosis of Alzheimer's disease (AD) from electroencephalograms (EEG). Three major effects of AD on EEG have been observed: slowing of the EEG, reduced complexity of the EEG signals, and perturbations in EEG synchrony. In recent years, a variety of sophisticated computational approaches has been proposed to detect those subtle perturbations in the EEG of AD patients. The paper first describes methods that try to detect slowing of the EEG. Next the paper deals with several measures for EEG complexity, and explains how those measures have been used to study fluctuations in EEG complexity in AD patients. Then various measures of EEG synchrony are considered in the context of AD diagnosis. Also the issue of EEG pre-processing is briefly addressed. Before one can analyze EEG, it is necessary to remove artifacts due to for example head and eye movement or interference from electronic equipment. Pre-processing of EEG has in recent years received much attention. In this paper, several state-of-the-art pre-processing tech- niques are outlined, for example, based on blind source separation and other non-linear filtering paradigms. In addition, the paper outlines opportunities and limitations of computational approaches for diagnosing AD based on EEG. At last, future challenges and open problems are discussed.