In this work we discuss the fault avoidance and the fault tolerance approaches for increasing the reliability of aerospace and automotive systems. This includes: the basic definitions/concepts (reliability, maintainability, availability, redundancy, etc.), and characteristics (a priori analysis, a posteriori analysis, physical/hardware redundancy, analytical/software redundancy, etc.) of both approaches, their mathematical background and models (exponential, Weilbull, etc.), their basic theory, their methods and techniques (fault trees, dependence diagrams, Markov chains, etc.), some of their standards (SAE-ARP4761, AC 25.1309, etc.) and simulation environments (Cafta, etc.), and their applications to the reliability analysis and reliability improvement of aerospace and automotive vehicles. This is illustrated by some examples driven from the aerospace and automotive industries. BASIC DEFINITIONS/CONCEPTS, TYPES, CHARA CTERISTICS, ETC. Reliability-The probability that a device or system will perform a required function under stated conditions for a stated period of time. This is the basic property of a system which we seek to enhance through the concept of fault tolerance. It is stated in statistical terms-as a probability-which reflects the fact that failures occur at unpredictable times. This establishes at the outset the fact that much of the analysis in this paper will have to be statistical in nature.