The topic of this paper is the exploration of the various characteristics of the wavelet tree data structure, a data structure that was initially proposed for text compression applications but has found a plethora of other uses in text indexing and retrieval. Issues concerning the efficient maintenance of the structure, plus its handling in various applications are explored. Our main aim is to provide to computer science researchers that would like to explore the specific area, an up-to-date comprehensive material covering a wide range of applications. This kind of up-to-date survey is missing from the current bibliography and we hope that it will help young researchers to get familiar with the notions of this research area.