Fault detection and diagnosis have gained central importance in the chemical process industries over the past decade. This is due to several reasons, one of them being that copious amount of data is available from a large number of sensors in process plants. Moreover, since industrial processes operate in closed loop with appropriate output feedback to attain certain performance objectives, instrument faults have a direct effect on the overall performance of the automation system. Extracting essential information about the state of the system and processing the measurements for detecting, discriminating, and identifying abnormal readings are important tasks of a fault diagnosis system. The goal of this dissertation is to develop such fault diagnosis systems, which use limited information about the process model to robustly detect, discriminate, and reconstruct instrumentation faults. Broadly, the proposed method consists of a novel nonlinear state and parameter estimator coupled with a fault detection, discrimination, and reconstruction system. The first part of this dissertation focuses on designing fault diagnosis systems that not only perform fault detection and isolation but also estimate the shape and size of the unknown instrument faults. This notion is extended to nonlinear processes whose structure is known but the parameters of the process are a priori uncertain and bounded. Since the uncertainty in the process model and instrument fault detection interact with each other, a novel two-time scale procedure is adopted to render overall fault diagnosis. Further, some techniques to enhance the convergence properties of the proposed state and parameter estimator are presented. The remaining part of the dissertation extends the proposed model-based fault diagnosis methodology to processes for which first principles modeling is either expensive or infeasible. This is achieved by using an empirical model identification technique called subspace identification for state-space characterization of the process. Finally the proposed methodology for fault diagnosis has been applied in numerical simulations to a non-isothermal CSTR (continuous stirred tank reactor), an industrial melter process, and a debutanizer plant.