More than 30 years ago, Epstein and Sobel introduced the Total Time on Test (TTT-) concept. During the last 10 years different generalizations of this concept have been defined and studied, e.g. the TTT-transform and the TTT-plot; a basic paper was presented by Barlow and Campo in 1975. Many of these generalizations have proven to be very useful in different areas of reliability, both from a theoretical and a practical point of view. The purpose of this expository paper is to present some of these generalizations and illustrate their value.