Many industrial heat transfer problems, nowadays, involve complex geometries and boundary conditions. In the last thirty years, developments in the numerical solution of coupled heat transfer and fluid flow problems are enormous and getting a reasonably accurate solution for such complex problems is now possible. However, it is important to note that in many heat and mass transport problems the issues such as solution accuracy, flexibility of the method used, complexity of the numerical method employed are still matters for discussion among the engineering community. In order to get a very accurate numerical solution, many researchers employ structured meshes in the solution of heat transfer problems. However, it is very difficult and often impossible to generate structured meshes for complex geometries. It is, therefore, important to promote unstructured mesh methods to achieve flexibility without compromising accuracy. In this paper, a brief overview of the use of the finite element method in solving combined heat transfer and fluid flow problems is given. A split method is discussed and its use in forced, natural and mixed convection problems is explained. Other available schemes for the solution of heat and fluid flow problems are also mentioned.