Automatic Character Recognition has wide variety of applications such as automatic postal mail sorting, number plate recognition and automatic form of reader and entering text from PDA's etc. Cursive script's Automatic Character Recognition is a complex process facing unique issues unlike other scripts. Many solutions have been proposed in the literature to solve complexities of cursive scripts character recognition. This paper present a comprehensive literature review of the Optical Character Recognition (OCR) for off-line and on-line character recognition for Urdu, Arabic and Persian languages, based on Hidden Markov Model (HMM). We surveyed all most all significant approaches proposed and concluded future directions of OCR for cursive languages.