Today the aircraft engine designing and development work is increasing drastically. Especially aircraft engines play a vital role in order to decide the aircrafts speed and its performance. Broadly turbojet, turboprop, turbo shaft and turbofan engines comes under the category of air breathing engines. Every engine has its own purpose and application. But modern aircrafts require much more advancements. Designing a new aircraft engine has been a really challenging task to the researchers. But giving a complete holistic view of aircraft engines and research gap would definitely help a lot to the new designers. Once identified the drawbacks of engine performance can be corrected in the future. For any new design of aircraft engine researchers are suggested to take Theoretical, Experimental and Numerical approaches. Therefore present paper makes an effort to review complete recent Theoretical, Experimental and Numerical approaches which are followed till date. Under all the three approaches all the air breathing engines have been clearly explained and solicited. The effort is to identify the gaps between different approaches which are hampering the process of engine development. The paper also gives the research gaps that need to be incorporated for effective performance enhancement of the aircraft engines for aeromechanical features.