The main objective of the present thesis is to develop mathematical models to discuss the boundary layer flows over a curved moving surface. These mathematical models are formulated in curvilinear coordinates system and then used to investigate the flow and heat/mass transfer characteristics for viscous and micropolar fluids. Additional features like influence of magnetic field, flow through porous media, thermal radiation effects, slip condition, heat generation/absorption, chemical reaction and nanofluids are also studied. The transformed boundary value problems consisting of highly nonlinear differential equations are solved numerically using the shooting and Kellar-box methods. The quantities of interest like fluid velocity, temperature, concentration, skin friction, heat and mass transfer rate at the wall are analyzed for various emerging parameters. It is found that by increasing the dimensionless radius of curvature, velocity and magnitude of the pressure distribution are decreased inside the boundary layer. Finally, a comparison of the present solutions with the existing results in the case of a flat stretching sheet is also presented.