The gas turbine engine's extreme conditions need a robust design to produce efficient energy and for reliable operation. Flow and thermal analysis are essential for complex aerodynamic and thermodynamic interaction during turbine performance. There is a need to understand and predict the temperature to make the gas turbine engine efficient. This paper will outline the numerical methods applied for primary cooling methods in gas turbine blades. These include impinging leading-edge cooling, internal cooling in the midsection, and pin fin in the trailing edge. The main objective of this paper is to understand the numerical research done on improving gas turbine cooling. The emphasis will be on understanding the present computational fluid dynamics (CFD) techniques applied for gas turbine cooling and further development. This paper briefly outlines the new conjugate heat transfer–based CFD modeling techniques that have evolved over the years due to recent computing power development.