At present achieving fuel economy and reducing emissions are the two main targets set by the automotive industries. The homogeneous charge compression ignition (HCCI) is an advanced combustion technology that is cleaner and more proficient than alternate kinds of combustion. Regardless of the way that the fuel conversion efficiency and NO𝑥emission of HCCI engine are more prominent in examination with conventional engines, HCCI combustion has a few fundamental issues, for example, concession combustion phase control, controlled auto-ignition, operating range, preparation of homogeneous charge, cold start and emissions of unburned hydro carbon (UHC), and carbon monoxide (CO) should be defeat for effective process of HCCI engine. Most of the researcher worked out on preparation of homogeneous fuel-air mixture. In this paper, review to give an overview on earlier work did on the external mixture formation methods and which are implemented and offered in the present years. The various methods of combustion phase control by HCCI combustion are also discussed and various Numerical investigations methods on HCCI engine are also presented.