Numerical simulations are performed to investigate the effect of the Reynolds number (Re) on flow over curved plates. Concave and convex plates, obtained by introducing curvature on a flat plate, are analyzed in the Reynolds number range 0.1  ≤ Re ≤ 120. It is observed that for a concave plate, the separation point is dependent on Re, while for a convex plate, the flow separates from the outermost tips for all Reynolds numbers. The analysis of time-averaged quantities reveals that concave and convex plates behave differently for the same Reynolds number. In the steady flow regime, visualization of streamlines reveals the presence of a recirculation bubble on the front side of the concave plate, even for the lowest Reynolds number (Re = 0.1). However, at higher Reynolds numbers (Re = 110, 120), the near wake of concave plate witnesses secondary and tertiary recirculating entities. The present simulations also report the unique phenomenon of vortex realignment and divergence of vortex street in the wake of a concave plate. For a convex plate, the vortex realignment is followed by the movement of upper and lower vortices as two parallel vortex streets. The existence of multiple instabilities is another highlight in the near and far wakes of the concave plate, some of which arise due to the secondary vortex interactions. A comprehensive analysis further reveals a handful of novel phenomenal occurrences in the wake of concave surfaces.