Spin-transfer effects induced by spin-polarized current in the spin valve structures present a platform for studying different static and dynamic magnetization states sustained or driven by current. Especially, it can excite some new magnetic states and cause magnetization reversal and precession, which offers some promising applications in data processing and microwave emission. However, most of researches so far have focused on the spin valve structure with parallel or perpendicular anisotropy. Compared with the spin valve structure with parallel or perpendicular anisotropy device, the spin valve structure with a tilted polarizer is also hopeful for its potential application in fast-switching and high-density magnetic recording. Moreover, the tilted polarizer provides a new way to control the spin torquedriven magnetization dynamics in spin valve structure. In this paper, the magnetization reversal and precession driven by the spin-transfer torque in spin valve structures with a perpendicular free layer and a tilted polarizer layer are investigated theoretically. By linearizing the Landau-Lifshitz-Gilbert equation including the spin-transfer torque, two coupled dynamically evolutive equations and new equilibrium directions are obtained. Performing stability analysis for all new equilibrium directions and taking [Co/Ni]4 multilayers as an illustrative example, we obtain the phase diagrams of magnetic states defined in parameter space spanned by external magnetic field and current density. Several magnetic states, including quasi-parallel stable states, quasi-antiparallel stable states, out-of-plane precession, and bistable states are distinguished in the phase diagrams. Through adjusting the magnitudes of current density and external magnetic field, the switching from stable states to precessional ones and the reversal between two stable states can be realized, and the reversal current increases with the external magnetic field increasing. Meanwhile, we portray the phase diagram of magnetic states defined in parameter space spanned by current density and the direction of tilted polarizer. In this case, the out-of-plane precession does not emerge as the current density and external magnetic field are relatively small. Affected by the directions of spin polarizer, the reversal current of magnetization is lowest when the direction of spin polarizer is parallel to the easy axis of free-layer, and is largest when the direction of spin polarizer is perpendicular to the easy axis of free-layer. Selecting the different directions of the polarized-layer magnetization provides an alternative way to improve the efficiency of current-driven microwave emitting and magnetization reversal. By solving temporal evolution equations numerically, the behaviors of different magnetic states are shown and the validities of the phase diagrams are confirmed.