The current status of computational capabilities for calculating viscous-inviscid transonic flows other than the solution of Navier-Stokes equations is presented. Techniques for solving transonic inviscid flows and compressible integral boundary layer methods are reviewed, and systems for strong viscous-inviscid interactions are described. Generally, the transonic viscous-inviscid interaction is characterized by a subcritical boundary layer with a supersonic outer stream. The thickening boundary layer produces a pressure rise which causes further thickening of the boundary layer. The physical flow is best modeled by direct coupling of the viscous and inviscid systems to allow immediate interaction between the shock wave and the boundary layer. It appears that the method of integral relations for the outer inviscid flow, combined with an integral boundary layer scheme, possesses such a capability. To facilitate the computation, an hybrid approach to the transonic inviscid solution, which consists of the finite difference method for solving the overall transonic inviscid potential flow field and the method of integral relations for solving Euler's equation in the shock region, is suggested. Finally, the application of the steady two-dimensional methods to the quasi two-dimensional problem on axisymmetric stream surface of a cascade flow at transonic speeds is discussed. (Author).