Controls of integrated gasoline engine and after-treatment systems are critical for fuel efficiency improvement and emission regulation. This paper aims to develop novel model-based Three-Way Catalytic converter (TWC) controls to reduce the fuel consumption and tailpipe emissions for a gasoline engine. A model-based dither control and a nonlinear model predictive control (MPC)-based control, are presented, respectively. The proposed TWC dither control utilizes a systematically designed dither cycle configuration (including dithering amplitude, offset, and frequency) based on a control-oriented model, with the capability to adapt the dither cycle configuration to various engine operating conditions. The MPC control can optimize engine air-fuel ratio (AFR) to maintain the oxygen storage of TWC at a desired level and thus meet the tailpipe NOx, CO and HC emission requirements. The efficacies of both model-based TWC controls are validated in simulation with MPC control improving CO emission conversion efficiencies by 8.42% and 4.85% in simplified US06 and UDDS driving cycles, when compared to a baseline dithering-based AFR control. Meanwhile, NOx emission conversion efficiency is maintained above the required limit of 95%, while the fuel efficiency remains at the same level as the baseline control methodology.