Understanding the physics of the pressure fluctuations induced by high-speed turbulent boundary layers (TBLs) is of major practical importance. The fluctuating pressure on aerodynamic surfaces of flight vehicles determines the vibrational loading of the vehicles and often leads to damaging effects as fatigue and flutter. The freestream pressure fluctuations radiated from the tunnel-wall TBLs are responsible for the genesis of freestream acoustic noise in conventional (i.e., noisy) supersonic and hypersonic wind tunnels. In this manuscript, wall and freestream pressure fluctuations induced by high-speed TBLs were characterized by direct numerical simulations (DNS). The DNS database covered a broad range of flow conditions (Mach number of $M_\infty = 2.5-14$, wall-to-recovery temperature ratio of $T_w/T_r = 0.18-1.0$, Reynolds number of $Re_\tau=450-1172$) and geometric configurations (flat plate, sharp circular cone, two dimensional channel, realistic wind-tunnel nozzle). The DNS overcame multiple experimental difficulties and provided access to wall and freestream pressure statistics that were difficulty to obtain otherwise, including the root-mean-square fluctuations and higher order moments (skewness and flatness) , probability density function , two-point correlation, convection speed, and coherence function. The study yielded useful insights into the physics of the boundary-layer-induced pressure field and provided critical assessment to reduced-order models such as the Corcos theory for modeling the wall pressure and the eddy-Mach-wave radiation theory for predicting the freestream acoustic pressure.