The surfaces of many plants and animals are covered with a variety of micro-textures such as ribs or 3D tubules which can control surface-mediated properties such as skin friction. Inspired by the drag reducing ability of these natural structures, especially the ribbed features on shark denticles, passive drag reduction strategies such as micro-fabricated riblet surfaces have been developed and studied. Microgroove textures on the surface of objects such as hulls, wings or inner surface of pipes which are aligned in the stream-wise direction have been shown to reduce the wall friction by 4 − 8%. The mechanisms suggested for this form of drag reduction are viscous retardation of the flow in the grooves (both laminar and turbulent) and the displacement of vortical structures away from the wall in turbulent flows. Due to their effectiveness in altering the boundary layer structure and reducing the viscous drag force, use of riblets have been banned in various competitions such as the America’s Cup. The current thesis work is partly focused on theoretical and numerical modelling (using the open source CFD package OpenFOAM) of the evolution of viscous boundary layers in the presence of various-shaped riblets (V-grooves as well as sinusoidal wrinkled surfaces) in high Reynolds laminar flow. We explore the effect of the dimensionless height to spacing of the grooves (aspect ratio) as well as the length of the wetted surface in the streamwise direction and how these change the total drag compared with a corresponding flat wall. We show that riblets retard the viscous flow inside the grooves and reduce the shear stress inside the grooves. But for this reduction to result in overall drag reduction, the riblet wall needs to be longer than a critical length. The total drag reduction achieved is a non-monotonic function of the aspect ratio of the riblets, with aspect ratios of order unity offering the largest reduction in the total drag. To eliminate the role of entrance effects, we additionally investigate the effect of stream-wise aligned riblet structures on fully-developed Taylor-Couette flow. We perform both experimental studies as well as time-dependent numerical simulations in both the laminar Couette and the Taylor vortex regime. We again explore the effect of the size of the riblets with respect to the geometry of the Taylor-Couette cell, as well as the aspect ratio of the riblet grooves and the shape of the grooves (V-groove, Rectangular, semi-circular, etc.). For the experiments, the cylindrical textured rotors are fabricated using 3D printing techniques and the rest of the Taylor-Couette cell is custom built using CNC machining. The test cell is then aligned and mounted on a stress-controlled rheometer to measure the velocity and the torque on the rotating inner cylinder. The numerical studies are performed using the open source CFD software package OpenFOAM to compare results and understand the physical mechanisms contributing to this drag reduction phenomenon. Again we observe a non-monotonic behavior for the reduction in torque as a function of the aspect ratio of the riblets tested, similar to the trend observed in the boundary layer analysis and we discuss the effect of changing the geometry of the flow as well as the riblet spacing on the changes in the total torque. When viewed holistically the results of these two studies show that, through careful design, a net reduction in viscous drag force can be robustly realized on micro-textured surfaces in high Reynolds number laminar flows through complex changes in near-wall stream-wise velocity profiles even in the absence of turbulent effects. The understanding of these changes can be effective in guiding the design of internal flows (pipes or ducts) and external flows (such as ship hulls, micro air vehicles or unmanned underwater vehicles) that are tailored and optimized to result in low frictional drag over the entire wetted surface in both laminar and turbulent regions.