This work examines the relative advantages and limitations of carrying out both simulation studies and experimental tests in order to evaluate the effectiveness of advanced algorithms for process control. Currently (and for good reason), the most common method of carrying out such evaluations is by simulation alone. Experimental testing is difficult and often leads to ambiguous conclusions. Nevertheless, there are some practical aspects of estimation and control algorithms which are revealed in experiments, but which never present themselves in simulation studies. Some of these are crucial for successful industrial implementation. The results reported here come from both simulation studies and experiments on three pilot plants available at Imperial College: a large-scale CO2 absorption/desorption plant; a single-cube full-scale reactor for gas-phase catalytic partial oxidation of hydrocarbons; a partially-simulated stirred reactor for general liquid-phase exothermic reactions. Examples which are illustrated include case studies on both linear and nonlinear algorithms of identification, estimation, and control. Some of the specific control algorithms which have been studied were: nonlinear geometric control, linear and nonlinear model predictive control, controllers based upon neural networks, and inferential controllers based upon on-line estimation of unmeasurable states. Comparison of simulation and experiment revealed that, in some cases, the experiments showed qualitatively different behaviour from even the most detailed simulation studies. Reasons are put forward as to why such large differences occasionally exist between the two types of tests. Among the most important reasons for these differences are the uncertain nature of plant-model mismatch in nonlinear systems, the crucial role of process and controller constraints (especially in experimental studies), and the sensitivity of some algorithms to the exact implementation of their calculated control action-something which is virtually impossible in practice. The case studies confirm the complementary nature of the important roles played by both simulation studies and detailed experimental tests in an industrially realistic environment.