Cell membranes are quasi-bidimensional soft systems formed by multipoles in an ordered array that can be polarized in an electric field. Consequently, electrostatic potentials emerge inside membranes, and membranes respond to external electric fields. From a mechanical perspective, membranes can be easily compressed-expanded, laterally deformed, and curved. Bending is particularly easy, and this kind of deformation translates to changes in the relative positions of the negative and positive charges, leading to strain gradient-induced polarization. Conversely, an external electric field gradient will exert a bending stress that translates to mechanical membrane deformation. These phenomena are described through membrane flexoelectricity. Here, we describe this property in lipid bilayers and cell membranes and summarize the studies in the field with emphasis on the effects promoted by membrane asymmetry.