Comparative studies of different inflow turbulent forcing effects on detonation front dynamics and the flow statistics are conducted through direct numerical simulations of turbulence–detonation/shock interactions. High-resolution bandwidth-optimized weighted essentially nonoscillatory scheme of spatial discretization and total variation diminishing temporal integration are used to solve the three-dimensional chemically reactive Navier–Stokes equations. The turbulent inflow vertical and entropic forcing effects on the three-dimensional detonation front and cellular structures are first analyzed. The influence of the inflow forcing on the generated regular cell patterns with diamond shape is compared. The vortex behind the detonation is quite different from that behind shock waves with the same inflow fluctuations. This also results in the larger increase of velocity variances downstream of detonation than the turbulence–shock case. The similar trend can also be found for the Taylor microscales. Effects of different inflow turbulence intensities are investigated. The irregular cellular detonations under vertical inflow forcing are also analyzed.