The EEG source localization which is used to localize the electrical activity of brain has been an active area of research as it provides useful information for study of brain's physiological, mental and functional abnormalities. This problem is called EEG inverse problem. The localization of the active sources needs the solution of ill posed EEG inverse problem. Since the foundation of this field till today, many methods have been developed with the aim of in-depth localization, high resolution, reduction in localization/energy error and decreased computational time. In this survey, EEG inverse problem is discussed with its primary to most developed and recent solutions. The introduction to the field along with the categorization of different solutions is provided. Also, the relative advantages and limitations for each method are discussed. Finally, the challenges and future recommendations are provided, in the end, for further improvement of EEG inverse problem in terms of resolution, computational power and localization error. © 2014 Elsevier Masson SAS. All rights reserved.