The rapid growth of digital libraries, e-governance, and internet based applications has caused an exponential escalation in the volume of ‘Big-data’ particularly due to texts, images, audios and videos that are being both archived and transmitted on a daily basis. In order to make their storage and transfer efficient, different data compression techniques are used in the literature. The ultimate motive behind data compression is to transform a big size data into small size data, which eventually implies less space while archiving, and less time in transferring. However, in order to operate/analyze compressed data, it is usually necessary to decompress it, so as to bring back the data to its original form, which unfortunately warrants an additional computing cost. In this backdrop, if operating upon the compressed data itself can be made possible without going through the stage of decompression, then the advantage that could be accomplished due to compression would escalate. Further due to compression, from the data structure and storage perspectives, the original visibility structure of the data also being lost, it turns into a potential challenge to trace the original information in the compressed representation. This challenge is the motivation behind exploring the idea of direct processing on the compressed data itself in the literature. The proposed survey paper specifically focuses on compressed document images and brings out two original contributions. The first contribution is that it presents a critical study on different image analysis and image compression techniques, and highlights the motivational reasons for pursuing document image analysis in the compressed domain. The second contribution is that it summarizes the different compressed domain techniques in the literature so far based on the type of compression and operations performed by them. Overall, the paper aims to provide a perspective for pursuing further research in the area of document image analysis and pattern recognition directly based on the compressed data.