In this paper, we discuss the model predictive control algorithms that are tailored for uncertain systems. Robustness notions with respect to both deterministic (or set based) and stochastic uncertainties are discussed and contributions are reviewed in the model predictive control literature. We present, classify and compare different notions of the robustness properties of state of the art algorithms, while a substantial emphasis is given to the closed-loop performance and computational complexity properties. Furthermore, connections between (i) the theory of risk and (ii) robust optimization research areas and robust model predictive control are discussed. Lastly, we provide a comparison of current robust model predictive control algorithms via simulation examples illustrating closed loop performance and computational complexity features. (C) 2017 Elsevier Ltd. All rights reserved.