The scale and complexity of computer-based safety critical systems pose significant challenges in the safety analysis of such systems. In this chapter, the authors discuss two approaches that define the state of the art in this area: failure logic modelling and behavioural modelling safety analyses. They also focus on Hierarchically Performed Hazard Origin and Propagation Studies (HiP-HOPS)—one of the advanced failure logic modelling approaches—and discuss its scientific and practical contributions. These include a language for specification of inheritable and reusable component failure patterns, a temporal logic that enables assessment of sequences of faults in safety analysis as well as algorithms for top-down allocation of safety requirements to components during design, bottom-up verification via automatic synthesis of Fault Trees and Failure Modes and Effects Analyses, and dependability versus cost optimisation of systems via automatic model transformations. The authors summarise these contributions and discuss strengths and limitations in relation to the state of the art.