Mathematical models of biochemical reaction networks are important tools in systems biology and systems medicine, e.g., to analyze disease causes or to make predictions for the development of effective treatments. Models are also used in synthetic biology for the design of circuits that perform specialized tasks. Prediction, analysis and design require plausible and reliable models, that is, models must reflect the properties of interest of the considered biochemical networks. One remarkable property of biochemical networks is robust functioning over a wide range of perturbations and environmental conditions. The intrinsic robustness of a network should be reflected into its associated mathematical model. The description and analysis of robustness in biochemical reaction networks are challenging, however, because accounting explicitly for the various types of structural, parametric and data uncertainty in the description of the models is not straightforward. Furthermore, system properties are typically inherently uncertain and often only given by qualitative or verbal descriptions that impede a straightforward and comprehensive mathematical analysis. In the first part of this overview article, network functions and behaviors of interest are formally defined, and different classes of uncertainties and perturbations are consistently described. The second part reviews frequently used mathematical formulations and presents the authors' recent developments for robustness analysis, estimation, and model-based prediction. One biochemical network model is used to illustrate the capabilities of various methods to deal with the different types of uncertainties and robustness requirements. (C) 2016 Elsevier Ltd. All rights reserved.