We present the most relevant works on jet engine design that utilize thermodynamic cycle of detonative combustion. Detonation engines of various concepts, pulse detonation, rotational and engine with stationary detonation wave, are reviewed. Main trends in detonation engine development are discussed. The most important works that carried out theoretical, experimental and computational research and their parametrical optimization are described. Relevant for nearest time problems and directions of research are formulated. [For "Detonation Jet Engine. Part 1--Thermodynamic Cycle," see EJ1115570.]