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 will show high-fidelity numerical results of supersonic spatially-developing turbulent boundary layers (SDTBL) subject to strong concave and concave curvatures and Mach = 2.86, which are of crucial importance in aerospace applications, such as unmanned high-speed vehicles, scramjets and advanced space aircrafts. The selected numerical tool is Direct Numerical Simulation (DNS) with high spatial/temporal resolution. The prescribed concave 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 extensive DNS information sheds important light on the transport phenomena inside turbulent boundary layers subject to strong deceleration or Adverse Pressure Gradient (APG) caused by concave walls as well as to strong acceleration or Favorable Pressure Gradient (FPG) caused by convex walls at different wall thermal conditions (i.e., cold, adiabatic and hot walls). Visualization of quadrant events (outward/inward interactions, ejections and sweeps) reveals a significant enhancement of those turbulent events in the concave and ramp wall. The supersonic expansion in the convex region induces an evident streamwise stretching over turbulent coherent structures (quasi-laminarization). The decrease of wall temperature (cooling wall condition) makes the turbulent structures more organized and anisotropic.