Reshotko has suggested that transition may be viewed as the response of a very complex three-dimensional nonlinear oscillator (the laminar boundary layer) to a random and often statistically nonuniform forcing function (the disturbances). The first objective of this study concerns the phenomenon of flow transition in boundary layers on turbine airfoils--from the onset of turbulence to the transition completion. Transition studies, though fundamental to fluid mechanics, are unique in gas turbine cascades because of the compounding factors that act not in individual isolation, but as a collective group and that constitute by-pass mechanisms not amenable to linear analyses from a mathematical point of view. The second objective is to evolve an engineering method to account for surface roughness effects on heat transfer and turbulent boundary layer analyses, which have heretofore been studied in fragments. Transition prediction in gas turbine boundary layer flows is critical in assessing the cooling requirements for gas turbine vanes and blades. This report summarizes the classical, fundamental findings in transition prediction for simplified geometrics and discusses empirical rules currently in use for gas turbine environments. Keywords: Airfoil boundary layer transition.