This paper aims at giving an overview of available results of state and parameter approaches for chemical and biochemical processes. It is largely organized as a tutorial and starts with a brief reminder concerning the design of extended Luenberger (ELO) and Kalman (EKO) observers, followed by an illustrative nonlinear observer algorithm. Evaluation of the performance of classical observers in presence of model uncertainties will serve as a basis for the motivation of designing asymptotic and interval observers, that do not require the knowledge of the process kinetics. The design of state observers with known kinetic models but uncertain kinetic parameters will then be considered via suggestions of improvements of the EKO and the introduction of two other types of observers (observers where the unknown parameters are used as design parameters; adaptive observers). Finally, the design of online parameter estimation schemes will be introduced. One of the objectives of the present survey is also to suggest new research directions. (C) 2003 Elsevier Ltd. All rights reserved.