Regulated exocytosis, which involves fusion of secretory vesicles with the plasma membrane, is an important mode of communication between cells. In this process, signalling molecules that are stored in secretory vesicles are released into the extracellular space. During the initial stage of fusion, the interior of the vesicle is connected to the exterior of the cell with a narrow, channel-like structure: the fusion pore. It was long believed that the fusion pore is a short-lived intermediate state leading irreversibly to fusion pore dilation. However, recent results show that the diameter of the fusion pore can fluctuate, suggesting that the fusion pore is a subject of stabilization. A possible mechanism is addressed in this article, involving the local anisotropicity of membrane constituents that can stabilize the fusion pore. The molecular nature of such a stable fusion pore to predict how interacting molecules (proteins and/or lipids) mediate changes that affect the stability of the fusion pore and exocytosis is also considered. The fusion pore likely attains stability via multiple mechanisms, which include the shape of the lipid and protein membrane constituents and the interactions between them.