P systems with active membranes constitute a very interesting model of computation, defined in the framework of Membrane Computing. Since their appearance, they have been used to solve computationally difficult problems (usually in the classes NP and PSPACE), due to their ability to generate an exponential size workspace in a polynomial number of time steps. Several computational complexity techniques have thus been applied to study their computing power and efficiency. During the talk, I will survey some of the techniques and the main results which have been obtained in the last few years by the group of Membrane Computing at the University of Milano-Bicocca (also known as the “Milano Team”), sometimes in collaboration with colleagues from the international Membrane Computing community.