This thesis describes computational fluid dynamic study of the wake behind thin flat plates at Reynolds numbers large enough for the formation of energetic structures and turbulence. The dynamically rich behavior of unsteady turbulent wake of bluff bodies consists of energetic and large-scale structures generated through flow instabilities, which have an anisotropic and geometry dependent topology. Large eddies are most important in characterizing the wake and provide the largest contribution to kinetic energy. The three-dimensional wake of thin flat plates positioned normal to a uniform flow is evaluated using Direct Numerical Simulations and Large Eddy Simulations. The flow around a 2D plate is examined at Re = 1200 and 2400 to characterize the wake and establish the dynamics of vortex formation and detachment processes. This is extended to the wake of finite aspect ratio (3D) thin flat plates at Re = 1200. The aspect ratios investigated are 3.2, 1.6 and 1.0. Flow topology eduction is carried out by examining the temporal evolution of aerodynamic forces and their phase-angles, as well as velocity and vorticity fields. Large-scale structures are investigated based on their topology, contributions to turbulent kinetic energy, and interaction with the surface pressure. The educed structures in the wake of 2D plates belong to three distinct regimes (H for high-, L for low-, and M for moderate-intensity vortex shedding) determined from periodicity of vortex shedding based on lift and drag fluctuations. The characteristics of previously identified H and L regimes were quantified, while introducing a new regime M. Formation and distortion of spanwise vortex rollers and streamwise vortex ribs coupled with Reynolds stress anisotropy and compression or stretching of the recirculation region characterize main differences among these regimes. The introduction of additional shear layers significantly alters the flow topology and vortex shedding process for 3D plates compared to 2D plates. Vortices are formed on longer edges of the plate, whereas shear layers on the shorter sides are carried away by the induced streamwise flow. This results in a single vortex shedding process. The vortex “peel-off” on shorter edges fixes the vortex detachment at sharp corners of the plate.