This paper considers two topics in mechanism design: fragility of optimal auctions and computationally constructive procedures for dynamic mechanisms. The first part of the paper considers the well studied topic in mechanism design of optimal auctions, i.e., auctions that produce maximal revenue. The design of an optimal auction in a general setting requires the principal to have complete knowledge of the probabilistic beliefs of the agents (bidders). This work shows that such an assumption leads to fragile designs in which a slight perturbation to these beliefs can alter the outcome of the auction significantly. We propose an alternative approach where the designer takes into account a nominal environment and provides incentives that are robust to perturbations on the beliefs of the agents. Using the theory of robust optimization, we find relevant uncertainty classes for which the proposed robust mechanisms have the same computational complexity as the nominal designs. The second part of the paper discusses dynamic mechanism design. Whereas standard mechanism design presumes a one shot scenario, dynamic mechanism design considers perpetual phenomena, e.g., the allocation of a limited resource to transient users. The dynamic mechanism problem has received considerable attention given the wealth of applications. Most work has concentrated on finding appropriate conditions according to which static designs have natural extensions to the dynamic setting. This paper considers optimal dynamic mechanisms using tools from robust control theory. In this framework the design of incentives for a desired social planner's policy reduces to the search of a storage function, analogous to synthesis problems involving dissipation inequalities. For specific structures, optimizing the incentives reduces to solving a linear program.