Microrobots can be used in the manipulation and precise positioning of micro-objects, as well as in several microelectronics applications. Microrobotics is primarily concerned with control problems of micro electromechanical systems (MEMS). Specific problems that one encounters when developing microrobotic systems and MEMS is the imprecision about the micro-robot’s dynamic model and the inability to measure specific state vector elements in it. This in turn signifies that the design of feedback controllers for such systems has to be sufficiently robust to compensate for unmodelled dynamics or for parametric uncertainty. To this end one can consider either model-free control methods of proven stability (such as adaptive neurofuzzy control schemes), or model-based control methods capable of eliminating the effects of modelling errors, parametric inconsistency and external perturbations (such as H-infinity control). Moreover, one has to implement state estimation-based feedback control methods, making use of robust state observers, that will allow for estimation of the entire state vector of the microrobot or MEMS through the processing of measurements from a small number of sensors. In particular, the chapter treats the following topics: (a) Adaptive neurofuzzy control of micro-actuators, (b) Nonlinear optimal control of underactuated MEMS.