Current-induced magnetization reversal via spin-orbit torques (SOTs) has been intensively studied in heavy-metal/ferromagnetic-metal/oxide heterostructures due to its promising application in low-energy consumption logic and memory devices. Here, we systematically study the function of Joule heating and SOTs in the current-induced magnetization reversal using Pt/Co/SmOx and Pt/Co/AlOx structures with different perpendicular magnetic anisotropies (PMAs). The SOT-induced effective fields, anisotropy field, switching field and switching current density (Jc) are characterized using electric transport measurements based on the anomalous Hall effect and polar magneto-optical Kerr effect (MOKE). The results show that the current-generated Joule heating plays an assisted role in the reversal process by reducing switching field and enhancing SOT efficiency. The out-of-plane component of the damping-like-SOT effective field is responsible for the magnetization reversal. The obtained Jc for Pt/Co/SmOx and Pt/Co/AlOx structures with similar spin Hall angles and different PMAs remains roughly constant, revealing that the coherent switching model cannot fully explain the current-induced magnetization reversal. In contrast, by observing the domain wall nucleation and expansion using MOKE and comparing the damping-like-SOT effective field and switching field, we conclude that the current-induced magnetization reversal is dominated by the depinning model and Jc also immensely relies on the depinning field.