Cryogenic cavitation affects the operation of liquid propulsion systems during the first phase of a launch. Its effects within orifices or turbopumps can range from mild instabilities to catastrophic damages to the structures, jeopardizing the launch itself. Therefore, to ensure the proper designing of propulsion systems, cavitation phenomena cannot be neglected. Although hydrodynamic cavitation has been studied for decades, the impact of the nature of the fluid has been sparsely investigated. Therefore, this review, beginning from the basic concepts of cavitation, analyzes the literature dedicated to hydrodynamic cryogenic cavitation through an orifice. Our review provides a clear vision of the state-of-the-art from experimental and modeling viewpoints, identifies the knowledge gaps in the literature, and proposes a way to further investigate cryogenic cavitation in aerospace science.