High reliability and availability is a requirement for most technical systems. Reliability and availability assurance methods based on probabilistic models is the topic addressed in this talk. Non-state-space solution methods are often used to solve models based on reliability block diagrams, fault trees and reliability graphs. Relatively efficient algorithms are known to handle systems with hundreds of components and have been implemented in many software packages. Nevertheless, many practical problems cannot be handled by such algorithms. Bounding algorithms are then used in such cases as was done for a major subsystem of Boeing 787. Non-state-space methods derive their efficiency from the independence assumption that is often violated in practice. State space methods based on Markov chains, stochastic Petri nets, semi-Markov and Markov regenerative processes can be used to model various kinds of dependencies among system components. However, the resulting state space explosion severely restricts the size of the problem that can be solved. Hierarchical and fixed-point iterative methods provide a scalable alternative that combines the strengths of state space and non-state-space methods and have been extensively used to solve real-life problems. We will take a journey through these model types via interesting real-world examples chosen from IBM, Cisco, Sun Microsystems, and Boeing. These methods and applications are fully described in a recently completed book: Reliability and Availability Engineering: Modeling, Analysis and Applications, Cambridge University Press, 2017.