Abstract part 1 Fault tree analysis (FTA) is a very prominent method to analyze the dependability of safety and economically critical assets, like power plants, data centers and web shops. FTA comprises a wide variety of methods and techniques and is being deployed by many companies, like NASA, ESA, Honeywell, Airbus, Toyota, etc. This tutorial addresses how fault trees can be used to model and analyze the dependability of complex systems. I will give an introduction to the most common quantitative and qualitative analysis techniques, their practical relevance and deployment in practical risk assessments. Abstract part 2 In this presentation, I will elaborate how the deployment of stochastic model checking can improve the capabilities of fault tree analysis, making them more powerful, flexible and efficient: I will present a compositional framework, where we can analyze a richer variety of questions; we obtain more compact models via bisimulation and graph rewriting techniques; and get more flexibility in the modeling power. In particular, I will show how one can incorporate maintenance strategies, a crucial aspect in reliability engineering. Finally, I will report on our experience with the application and validation of these techniques in industrial practice; in particular in the railroad and nuclear domain.