Abstract: A review on the methods for predicting internal flowfield and designing aerodynamic shape of transonic centrifugal compressor is given in this paper.In general,the development of the transonic centrifugal compressor lags behind that of transonic axial compressor.However,the transonic centrifugal compressor will be widely applied to powerplant of helicopters,the turbochargers of vehicles and compressors of petroleum chemical industry etc.Thanks to an urgent need of engineering practice,it can be prophesied that transonic centrifugal compressor will make great progress within the coming several decades.At present,inviscid calculation method with a distributed loss model (or boundary layer calculation) is a main tool to predict or design the transonic centrifugal compressor.However,along with development of computer,3D Navier Stokes solver may be applied in engineering practice within the coming decade.In the inviscid calculation method,the S1 and S2 stream surface caulculation method is the most improtant method at present.When the S1 and S2 method is used,the computer memory required is smaller and the CPU time consumed is shorter than 3D Navier Stokes Solver.Of course, the S1 and S2 method is suitable only for non separated flow condition at design point.As for design methods of the transonic centrifugal compressor,it is necessary to make full use of experience of axial compressor designing.