This paper presents an overview of the recent developments of modifier-adaptationschemes for real-time optimization of uncertain processes. These schemes have the ability to reach plant optimality upon convergence despite the presence of structural plant-model mismatch.Modifier Adaptation has its origins in the technique of Integrated System Optimization and Parameter Estimation, but differs in the definition of the modifiers and in the fact that no parameter estimation is required. This paper reviews the fundamentals of Modifier Adaptation and provides an overview of several variants and extensions. Furthermore, the paper discusses different methods for estimating the required gradients (or modifiers) from noisy measurements. We also give an overview of the application studies available in the literature. Finally, the paper briefly discusses open issues so as to promote future research in this area.