Monitoring and control of batch pulp digesters, which convert wood chips to pulp by Kraft process are discussed. The Kappa number, which represents the extent of delignification, is the key controlled variable, which cannot be measured on-line and must be estimated through secondary liquor measurements. Given a fixed batch time, the final Kappa number should be as close to the target Kappa number as possible, despite errors in the initial state estimates and input disturbances. To fulfill this objective, a state-observer-based model-predictive controller is designed using a detailed nonlinear dynamic model of the digester. The extended Kalman filter (EKF) using on-line measurements of various liquor characteristics is capable of recovering from significant errors in the initial state estimates. In addition, the EKF is shown to be robust to the errors in the covariance matrices and most model parameters, but quite sensitive to some model parameter errors. Coupled with the EKF, a finite-horizon model predictive controller (MPC) based on successive linearization of the nonlinear pulping model, is found to work efficiently for controlling the Kappa number and batch time.