This project is concerned with theoretical investigations of coupled viscous incompressible flows in the presence of porous media or the flows that take place entirely in a porous medium. Such flows have been the subject of extensive investigation in the literature during last several decades apparently due to practical applications in a number of disciplines related to engineering and technology. Several transport models such as classical Darcy law, Brinkman-extended Darcy model, Forchheimer-extended Darcy model, have been generally used to describe flow in a porous medium, together with a host of matching conditions at one or more interfaces. Three different basic flow problems, both steady and unsteady, including heat transfer aspects, have been investigated in the project. They are related to either type of the above mentioned flows. In the first problem, unsteady simultaneous flows of two immiscible fluids over a porous bed of finite thickness and caused by the oscillations, in its own plane, of the rigid plate bounding the porous medium has been studied. In the second problem, steady flow and heat transfer aspects have been investigated for the Poiseuille flow of two immiscible fluids in a straight channel bounded below and above by porous media of different permeability. The last problem considers steady mixed convection, subject to Boussinesq approximation, in a porous vertical channel saturated with a single fluid. Using suitable porous media models, exact solutions of the governing momentum and energy equations for each flow problem, subject to an appropriate set of boundary and, where applicable, matching conditions, have been obtained. In order to showcase the effects of a host of non-dimensional governing parameters that arise during the analysis, plots of flow variables such as velocity, temperature have been exhibited and discussed in a number of cases of interest. Some results from the literature have also been extended.