The keys factor in making wind power one of the main power sources to meet the world's growing energy demands is the reliability improvement of wind turbines (WTs). However, the eventuality of fault occurrence on WT components cannot be avoided, especially for doubly-fed induction generator (DFIG) based WTs, which are operating in severe environments. The maintenance need increases due to unexpected faults, which in turn leads to higher operating cost and poor reliability. Extensive investigation into DFIG internal fault detection techniques has been carried out in the last decade. This paper presents a detailed review of these techniques. It discusses the methods that can be used to detect internal electrical faults in a DFIG stator, rotor, or both. A novel sorting technique is presented which takes into consideration different parameters such as fault location, detection technique, and DFIG modelling. The main mathematical representation used to detect these faults is presented to allow an easier and faster understanding of each method. In addition, a comparison is carried out in every section to illustrate the main differences, advantages, and disadvantages of every method and/or model. Some real monitoring systems available in the market are presented. Finally, recommendations for the challenges, future work, and main gaps in the field of internal faults in a DFIG are presented. This review is organized in a tutorial manner, to be an effective guide for future research for enhancing the reliability of DFIG-based WTs.