Reliability is an important issue in power systems and historically has been assessed using deterministic criteria and indexes. However, these approaches can be, and in many cases have been, replaced by probabilistic methods that are able to respond to the actual stochastic factors that influence the reliability of the system. In the days of global, completely integrated and/or nationalized electricity supply industries, the only significant objective was the reliability seen by actual end users. Also, the system was structured in a relatively simple way such that generation, transmission, and distribution could be assessed as a series of sequential hierarchical levels. Failures at any level could cause interruptions of supply to the end user. All planning and operational criteria were intended to minimize such interruptions within economic limits. The system has been, or is being, restructured and now many individual parties are involved, often competitively, including generators, network owners, network operators, energy suppliers, regulators, as well as the end users. Each of these parties has a need to know the quality and performance of the system sector or subsector for which they are responsible. Therefore, there is now a need for a range of reliability measures; the actual measure(s) needed varying between the different system parties. This paper addresses these issues and, in particular, reviews existing approaches and how these may be used and/or adapted to suit the needs and the required indexes of the new competitive industry and the different parties associated with it.