High performance liquid rocket engines require cooling to maintain structural integrity of the combustion chamber which is exposed to high thermal and environmental loads. For many systems, this is achieved by means of regenerative cooling, where a coolant flows through passages around the chamber wall whilst extracting heat from the wall. A novel production technique that is often considered for this is metal additive manufacturing (AM). The use of additive manufacturing opens up new opportunities for engine design, which can result in more competitive designs, from both a technical and economical perspective. This paper provides a detailed literature review on the current state-of-the-art, challenges, and opportunities for designing additively manufactured liquid rocket engines by means of laser powder bed fusion or powder-based and wire-based directed energy deposition (DED) techniques. A detailed, systematic explanation is provided on the steps involving the creation of additively manufactured thrusters including the process considerations, AM techniques and post-processing operations.