Unsteady 3D turbulent boundary layers that evolve along the flow direction exhibit a streamwise non-homogeneous condition and pose enormous computational challenges. The reasons are as follows: (i) full spectrum resolution of turbulence, (ii) accurate time-dependent inflow turbulence information, and (iii) compressibility effects. Moreover, accounting for the effects of wall-curvature driven pressure gradient adds significant complexity to the problem. In this video, we show numerical results of supersonic spatially-developing turbulent boundary layers (SDTBL) subject to strong concave (delta/R = -0.083) and very strong convex (delta/R = +0.17) wall curvatures, which are of crucial importance in aerospace applications, such as unmanned high-speed vehicles, scramjets and advanced space aircrafts. The freestream Mach number is 2.5. The selected numerical tool is Direct Numerical Simulation (DNS) with high spatial/temporal resolution. The prescribed curved geometry is based on the experimental study by Donovan et al. (J. Fluid Mech., 259, 1-24, 1994). Turbulent inflow conditions are based on extracted data from a previous DNS over a flat plate (precursor). The most important observation in supersonic boundary layers subject to concave curvature is the presence of outer secondary peaks in streamwise velocity fluctuations u’, since Adverse Pressure Gradient (APG) energizes the outer turbulent structures and turbulence production. Presence of quasi-laminarization downstream of the convex curvature (strong Favorable Pressure Gradient or FPG) in spite of the moderate Reynolds number.