Nothing is more exciting to a scientist than realizing that his/her areas of expertise are developing and that the state-of-the-knowledge yesterday is outdated today. The distinguished philosopher Ernst Mach first reported the phenomenon of shock wave reflection over 125 years ago in 1878. The study of this fascinating phenomenon was then abandoned for a period of about 60 years until Professors John von Neumann and Bleakney initiated its investigation in the early 1940s. Under their supervision, 15 years of intensive research related to various aspects of the reflection of shock waves in pseudosteady flows were carried out. It was during this period that the four basic shock wave reflection configurations, regular, single-Mach, transitional-Mach and double-Mach reflections, were discovered. Then, for a period of about 10 years from the mid-1950s until the mid-1960s, the investigation of the reflection phenomenon of shock waves was kept on a low flame all over the world (e.g. Australia, Japan, Canada, USA, USSR, etc.) until Professor Tatyana Bazhenova from the USSR, Professor Irvine Israel Glass from Canada, and Professor Roy Henderson from Australia re-initiated the study of this and related phenomena.