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In this lecture, the recent developments of the authors in the field of dynamical integrity applied to Micro-Electro-Mechanical-Systems (MEMS) are reviewed.The dynamical integrity was proposed by Thompson in the 90 and further developed by Lenci and Rega in the last decade.It is aimed at paralleling the classical concept of Lyapunov stability with a modem point of view in which the robustness of the attractor is discussed based on the dimension and of the topology of its basin of attraction.It is motived by the observation that when the basin of attraction is too small, or too fractal, small dynamical perturbations, always present in real life, will cause the disappearance of the attractor, with the dynamics that may jump on another (dominating)attractor, or suddenly leading to collapse.