Over the course of the history of today's rockets, liquid rocket engines have been used as primary propulsion for most space launch vehicles and early ballistic missiles. The visions of historical figures such as Tsiolkovsky, Goddard, and Oberth have become reality, resulting in humans reaching the moon and space exploration programs that stretch beyond the earth's orbit. A liquid rocket engine uses fuel and oxidizer in liquid form. Various combinations of liquid propellants have been characterized, tested, and flown. Engines are also classified according to the engine power cycle, which determines how the propellants reach the combustion chamber. Liquid rocket engines utilize numerous design power cycles and propellants depending on the application and design requirements. This chapter provides an overview of liquid rocket propulsion. Key historic achievements associated with pioneering efforts and development of large operational liquid rocket engines are first discussed. The fundamentals of liquid rocket engines are then described along with underlying design theory and practical experience. Lastly, the classifications of liquid rocket engines are provided in terms of application, engine cycle, and propellant combination. Keywords: liquid propulsion; history; fundamentals; liquid rocket engine; classifications; liquid propellant; monopropellant; bipropellants; cryogenic propellant; storable propellant; hypergolic propellant; mixture ratio; engine components; propellant tank; propellant feed system; engine cycle; pressure fed; gas generator; preburner; staged combustion; expander; turbopump; injector; thrust chamber; nozzle; propellant valve; thrust vector control; thrust; specific impulse