Writer identification is a wide-spreading biometric which can be used as a legitimate mean to identify an individual. It facilitates the experts to automatically identify the person in many security concerns applications such as forensic science. Due to this, much attention has been drawn in this field from the last few decades. On the basis of input text, it can have various forms like online, offline, text-dependent or text-independent writer identification. The paper will present a systematic study on text-dependent and text-independent writer identification of handwritten text images for various Indic and non-Indic scripts. The various segmentation techniques used to segment handwritten text are also presented in detail. The various datasets available for researchers are given for various scripts such as English, Arabic, Chinese, Japanese, Dutch, Farsi, Devanagari, Bangla, and Kannada discussed by doing exhaustive analysis of various studies. We hope that our research will be helpful in giving better understanding of the area and provides various directions for further research.