The sudden outage of a transformer due to a fault can cause irreparable damage to the electricity industry. Hence, by conducting momentarily inspections of the transformer's condition, faults can be promptly detected, and the transformer can be disconnected from the power grid to prevent subsequent failures in this equipment. Detecting faults at an early stage can also result in reduced repair costs. One recent promising technique for fault detection is Frequency Response Analysis (FRA), which compares the transformer's response in healthy and faulty conditions for understanding the occurrence of transformer faults. This paper presents a comprehensive and accurate modeling approach for the behavior of the transformer at different frequencies, followed by an exposition of the requirements for implementing this method in order to find the fault type, severity, and location. Additionally, various methods for analyzing the results of frequency response are introduced and discussed. In this regard, attempts have been made to introduce advanced complementary methods to address the weaknesses and limitations of the frequency response method. Finally, the concepts are summarized, and suggestions for further research with applications in this field are presented and compared.