We have proposed a new approach based on energy gradient concept for the study of flow instability and turbulent transition in parallel flows in our previous works. It was shown that the disturbance amplitude required for turbulent transition is inversely proportional to Re, which is in agreement with the experiments for imposed transverse disturbance. In present study, the energy gradient theory is extended to the generalized curved flows which have much application in turbomachinery and other fluid delivery devices. Within the frame of the new theory, basic theorems for flow instability in general cases are provided in details. Examples of applications of the theory are given from our previous studies which show comparison of the theory with available experimental data. It is shown that excellent agreement has been achieved for several configurations. Finally, various prediction methods for turbulent transition are reviewed and commented.