Arabic script classification is a complex area of research in the field of computer vision. The issue of offline Arabic script classification has been a concern of many researchers interest currently as it is assumed that online Arabic script recognition is comparatively simple and significant achievements have been attained. Numerous researchers deal with these issues evolved in pre-processing and post-processing techniques of Arabic script and presented various approaches to improve its accuracy rate. However, offline Arabic script classification and its related issues are still fresh. In this paper, we focus on pre-processing to post-processing techniques and highlight several issues in each phase in order to highlight need of high classification performance for Arabic script classification (offline and online). Additionally, top experimental results are reported, discussed and compared, and current challenges are also discussed. Finally, online versus offline Arabic script recognition achievements are also compared.