Membrane systems were introduced by Gh. Paun in 1998 as a class of distributed parallel computing devices of biochemical type, inspired from the functioning of living cells. Since then, they have been the subject of various studies, aimed at investigating and point out many aspects related to their computational power and efficiency. More recently, the model has been applied within the field of systems biology, for the modelling of complex biological systems and the analysis of their dynamics. In this paper, we present a class of membrane systems where probabilities (dynamically changing in time) are associated with the rules governing the evolution of the system, and we show how this model can be used to describe an oscillating process, the Belousov-Zhabotinskii reaction. Then, we discuss about the recent extensions of this model and its latest applications.