"The envelope of living cell is a lipid membrane. It is rather difficult to break, to ensure cell survival when under mechanical stress. However, in many events of cell life, the membrane needs to be broken in a controlled manner. It is the case in Endocytosis, when membrane carriers budding from the plasma membrane need to be separated from the plasma membrane, in order to uptake external components needed for the cell life. This reaction is called fission. It is also the case at the final step of cell division, cytokinesis, when the connecting membrane bridge between the two daughter cells is broken in a process called abscission. Even if fission and abscission machineries have been identified and are different, the reaction by which they break membranes should be the same, but is still unknown. By using membrane physics concepts and tools, we will investigate the mechanics of these two fission machineries. As they have different dynamics (tens of seconds for fission, tens of minutes for abscission), different scales (tens of nanometers for fission, microns for abscission) and different topology (fission machinery works from outside the neck, abscission machinery works from inside the neck), we will: 1-explain how each machinery breaks membranes, 2-find essential parameters that control all membrane fission reactions. We will thus draw a mechanical framework to then understand the role of keyfactors in all membrane fission reactions of cells."