Future space exploration missions will require the synergistic integration of potentially lightweight, high thrust producing, and environmentally sustainable rocket engines. This article guides through one such capable rocket engine, the cryogenic propulsion rocket engine and some cutting-edge characteristics and novel engineering advancements affiliated with it. A typical cryogenic-propulsion rocket engine works similarly to all other LPRE's (Liquid Propellant Rocket Engines), in which the primary fluid (Cryogenic fuel 1) reacts chemically to get vaporized and get ignited by an oxidizer to provide extremely hot rocket thrust that escapes the engine nozzle and generates thrust from the combustion process. Considerable efforts have been made to optimize the engine's performance and reliability in order to utilize the most desirable output from it. Therefore, a brief overview of the different models and research approaches associated with it to provide predictions and results about the stability, dynamics, and cooling characteristics of the given engine configuration is presented.