This study investigates the current-driven dynamics of chiral ferromagnetic domain walls (DWs) in ultrathin metallic ferromagnets sandwiched between a heavy metal and an oxide. The Dzyaloshinskii-Moriya interaction (DMI) stabilizes chiral DWs with a Néel configuration and left-handed chirality, enabling highly efficient current-driven motion. Spin torque from the spin Hall effect (SHE) drives DWs in opposite directions in Pt/CoFe/MgO and Ta/CoFe/MgO, which can only be explained by the Néel configuration. The DW chirality and rigidity were confirmed through current-driven DW dynamics under magnetic fields applied perpendicular and parallel to the spin spiral. The results resolve controversies in experimental findings and highlight a new path for interfacial spintronic device design. Current-controlled DW displacement underpins emerging spintronic memory and logic devices. In out-of-plane magnetized ferromagnets between an oxide and a heavy metal, current-induced DW motion is anomalously efficient. This is attributed to a Rashba effective field stabilizing Bloch DWs, allowing high-speed motion via conventional spin-transfer torque (STT). However, current-induced DW motion is absent in symmetric Pt/Co/Pt stacks, and semiclassical transport calculations suggest the spin-polarized current in ultrathin Co is vanishingly small. Moreover, DWs in Pt/Co/oxide move against electron flow, contrary to STT action. These results suggest that conventional STT contributes negligibly to DW dynamics in these ultrathin structures, and interfacial phenomena are instead responsible. The Rashba field lacks the correct symmetry to drive DWs directly, and the SHE in the adjacent heavy metal has emerged as an alternative mechanism. SHE-driven spin accumulation at the heavy-metal/ferromagnet interface generates a Slonczewski-like torque strong enough to switch uniformly-magnetized films. However, Bloch DWs expected in typical nanowire geometries have their plane oriented perpendicular to the nanowire axis, in which case the Slonczewski-like torque vanishes. This behavior was recently confirmed in asymmetric Pt/Co/Pt stacks in which the SHE-induced torques from the Pt layers did not cancel completely. In that case, current-assisted DW depinning was observed when an applied field rotated the DW plane towards the current axis, but up-down and down-up DWs were driven in opposite directions and the current had no effect in the absence of the bias field. The SHE alone is therefore incapable of uniformly driving trains of DWs in devices, and is insufficient to explain the high spin-torque efficiencies and DW velocities observed in Pt/Co/oxide without applied fields. Here, we characterize current-induced torques and DW dynamics in out-of-plane magnetized Pt/CoFe/MgO and Ta/CoFe/MgO stacks that are nominally identical except for the heavyThis study investigates the current-driven dynamics of chiral ferromagnetic domain walls (DWs) in ultrathin metallic ferromagnets sandwiched between a heavy metal and an oxide. The Dzyaloshinskii-Moriya interaction (DMI) stabilizes chiral DWs with a Néel configuration and left-handed chirality, enabling highly efficient current-driven motion. Spin torque from the spin Hall effect (SHE) drives DWs in opposite directions in Pt/CoFe/MgO and Ta/CoFe/MgO, which can only be explained by the Néel configuration. The DW chirality and rigidity were confirmed through current-driven DW dynamics under magnetic fields applied perpendicular and parallel to the spin spiral. The results resolve controversies in experimental findings and highlight a new path for interfacial spintronic device design. Current-controlled DW displacement underpins emerging spintronic memory and logic devices. In out-of-plane magnetized ferromagnets between an oxide and a heavy metal, current-induced DW motion is anomalously efficient. This is attributed to a Rashba effective field stabilizing Bloch DWs, allowing high-speed motion via conventional spin-transfer torque (STT). However, current-induced DW motion is absent in symmetric Pt/Co/Pt stacks, and semiclassical transport calculations suggest the spin-polarized current in ultrathin Co is vanishingly small. Moreover, DWs in Pt/Co/oxide move against electron flow, contrary to STT action. These results suggest that conventional STT contributes negligibly to DW dynamics in these ultrathin structures, and interfacial phenomena are instead responsible. The Rashba field lacks the correct symmetry to drive DWs directly, and the SHE in the adjacent heavy metal has emerged as an alternative mechanism. SHE-driven spin accumulation at the heavy-metal/ferromagnet interface generates a Slonczewski-like torque strong enough to switch uniformly-magnetized films. However, Bloch DWs expected in typical nanowire geometries have their plane oriented perpendicular to the nanowire axis, in which case the Slonczewski-like torque vanishes. This behavior was recently confirmed in asymmetric Pt/Co/Pt stacks in which the SHE-induced torques from the Pt layers did not cancel completely. In that case, current-assisted DW depinning was observed when an applied field rotated the DW plane towards the current axis, but up-down and down-up DWs were driven in opposite directions and the current had no effect in the absence of the bias field. The SHE alone is therefore incapable of uniformly driving trains of DWs in devices, and is insufficient to explain the high spin-torque efficiencies and DW velocities observed in Pt/Co/oxide without applied fields. Here, we characterize current-induced torques and DW dynamics in out-of-plane magnetized Pt/CoFe/MgO and Ta/CoFe/MgO stacks that are nominally identical except for the heavy