This chapter is devoted to liquid propellant rocket systems, including bi-propellant rocket engines, monopropellant, and bi-modal thrusters. An overview of their applications includes the propellant characteristics that rockets consume, classified as cryogenic, storable, hyperbolic, and green propellants. The exposition provides a summary of the propulsion requirements for launch vehicles and for spacecraft. A review of the most important chemical rocket engines utilized as boosters, main and final stages for launch vehicles, and on-board thrusters to maneuver spacecraft while in deep space, gives a perspective on the advantages of each type. Tables with performance data for many launch systems and in-space propulsion from around the world are given to compare their capability. The chapter concludes with a discussion of real rocket engines, addressing propellant injection and fed systems approaches, combustion chamber sizing and nozzle shapes, discussing rocket component design issues including requirements for nozzle area ratio for gas expansion, with and without nozzle extensions.