Learning to race autonomously is a challenging problem. It requires perception, estimation, planning, and control to work together in synchronization while driving at the limit of a vehicle's handling capability. Among others, one of the fundamental challenges lies in predicting the vehicle's future states like position, orientation, and speed with high accuracy because it is inevitably hard to identify vehicle model parameters that capture its real nonlinear dynamics in the presence of lateral tire slip. We present a model-based planning and control framework for autonomous racing that significantly reduces the effort required in system identification. Our approach bridges the gap between the design in a simulation and the real world by learning from on-board sensor measurements. Thus, the teams participating in autonomous racing competitions can start racing on new tracks without having to worry about tuning the vehicle model.