Fault tree or root cause analysis (FTA) is the most often used graphical deductive system analysis. It is by now the working horse in all fields with higher demands regarding reliability, availability, safety, and availability. It is increasingly also used in the domain of engineering resilience for assessing sufficient efficient response to expectable disruptions in terms of time needed to detect the disruption, to stabilize the system, and to repair or respond and recover. FTAs are conducted in several steps: identification of the goal of the analysis, of relevant top events to be considered, system analysis, FTA graphical construction using construction principles and rules, translation into Boolean algebra, determination of minimal cut sets (top-down and bottom-up), probabilistic calculation of top events (using the inclusion–exclusion principle), importance analysis, and executive summary. Each step is illustrated and several computation examples are provided. Major advantages of FTA include its targeted deductive nature that focuses on the system understanding and modeling used for the analysis by working in failure and success space as appropriate, the option to conduct the analysis qualitatively and quantitatively, and the evaluation options in terms of critical root cause combinations and minimal cut sets as determined by various importance measures. Further developments of FTA shortly discussed include its application to security issues in terms of attack trees, its application to the cybersecurity domain by typically assuming that most possible events actually occur, and time-dependent FTA (TDFTA). TDFTA goes beyond considering system phase- or use case-specific applications of FTA by considering time-dependent system states. Typically, such approaches are based on Markov or Petri models of systems. Another topic is to combine Monte Carlo approaches or fuzzy theory (fuzzification) to fault tree. Using distributions instead of failure probabilities allows to consider statistic uncertainties and deep uncertainties within FTA models of systems. In addition, several application examples are provided, in particular, how to use importance measures to identify component improvements that lead to the most efficient and economic improvement of systems.