Model predictive control (MPC) is indisputably one of the rare modern control techniques that has significantly affected control engineering practice due to its unique ability to systematically handle constraints and optimize performance. Robust MPC (RMPC) is an improved form of the conventional MPC that is intrinsically robust in the face of uncertainty. The main objective of RMPC is to devise an optimization based control synthesis method that accounts for the intricate interactions of the uncertainty with the system, constraints and performance criteria in a theoretically rigorous and computationally tractable way. RMPC has become an area of theoretical relevance and practical importance, but still offers the fundamental challenge of reaching a meaningful compromise between the quality of structural properties and the computational complexity.