This paper reviews and provides perspectives on the design of nonlinear model predictive control systems for polynomial systems. General nonlinear systems can often be rewritten exactly as polynomial systems or approximated as polynomial systems using Taylor series. This paper discusses the application of model predictive control (MPC) to these types of systems. After MPC problem for discrete-time polynomial systems is formulated as a polynomial program, moment-based and dual-based sum-of-squares (SOS) algorithms and their relationship are described as two promising methods for solving the polynomial programs to global optimality. Finally, future directions for research are proposed, including real-time, output-feedback, and robust/stochastic polynomial MPC.