Fault tree analysis (FTA) is a widely used method for analyzing a system’s failure logic and calculating overall reliability. However, application of conventional FTA has some shortcomings, e.g. in handling the uncertainties, allowing the use of linguistic variables, and integrating human error in failure logic model. Hence, Fuzzy set theory has been proposed to overcome the limitation of conventional FTA. Fuzzy logic provides a framework whereby basic notions such as similarity, uncertainty and preference can be modeled effectively.The aim of this paper is to present a review of the concept of fuzzy theory with fault tree analysis and their applications since 1981, to reflect the current status of Fuzzy Fault Tree Analysis (FFTA) methodologies, their strengths, weaknesses, and their applications. This paper explains the fundamentals of fuzzy theory and describes application of fuzzy importance for using FFTA. The concept of the failure possibility and uncertainty analysis by using FFTA is discussed, and concludes with discussion on the application of FFTA in different fields. The review reveals the effectiveness of the FFTA in comparison with conventional FTA, when there is inadequate amount of accurate reliability oriented information.