Abstract Ernst Mach recorded experimentally, in the late 1870s, two different shock-wave reflection configurations and laid the foundations for one of the most exciting and active research field in an area that is generally known as Shock Wave Reflection Phenomena. The first wave reflection, a two-shock wave configuration, is known nowadays as regular reflection, RR, and the second wave reflection, a three-shock wave configuration, was named after Ernst Mach and is called nowadays Mach reflection, MR. A monograph entitled Shock Wave Reflection Phenomena, which was published by Ben-Dor in 1990, summarized the state-of-the-art of the reflection phenomena of shock waves in steady, pseudo-steady and unsteady flows. Intensive analytical, experimental and numerical investigations in the last decade, which were led mainly by Ben-Dor's research group and his collaboration with Chpoun's, Zeitoun's and Ivanov's research groups, shattered the state-of-the-knowledge, as it was presented in Ben-Dor (Shock Wave Reflection Phenomena, Springer, New York, 1991), for the case of steady flows. Skews's and Hornung's research groups joined in later and also contributed to the establishment of the new state-of-the-knowledge of the reflection of shock waves in steady flows. The new state-of-the-knowledge will be presented in this review. Specifically, the hysteresis phenomenon in the RR↔MR transition process, which until the early 1990s was believed not to exist, will be presented and described in detail, in a variety of experimental set-ups and geometries. Analytical, experimental and numerical investigations of the various hysteresis processes will be presented.