Risk assessment methods have been widely used in various industries, and they play a significant role in improving the safety performance of systems. However, the outcomes of risk assessment approaches are subject to uncertainty and ambiguity due to the complexity and variability of system behaviour, scarcity of quantitative data about different system parameters, and human involvement in the analysis, operation, and decision-making processes. The implications for improving system safety are slowly being recognised; however, research on uncertainty handling during both qualitative and quantitative risk assessment procedures is a growing field. This paper presents a review of the state of the art in this field, focusing on uncertainty handling in fault tree analysis (FTA) based risk assessment. Theoretical contributions, aleatory uncertainty, epistemic uncertainty, and integration of both epistemic and aleatory uncertainty handling in the scientific and technical literature are carefully reviewed. The emphasis is on highlighting how assessors can handle uncertainty based on the available evidence as an input to FTA.