Flexoelectricity provides an exact relationship between electric and mechanical degree of freedom of a bilayer membrane, i.e. between transmembrane voltage and membrane curvature. Detailed studies by means of laser stroboscopic interferometry technique of direct flexoelectric effect in dipolar, zwitterionic and charged black lipid membranes (BLMs) and first observation of converse flexoelectric effect in an uranyl acetate-stabilized BLM are reviewed and theoretically interpreted. A new effect also involving another, optical degree of freedom of BLM, i.e. photo-flexoelectricity, was discovered very recently. It is observed in a composite BLM containing in-situ generated photo-semiconductor CdS nanosized particles (mimicking integral proteins of biomembranes) upon bandgap illumination. Light-dependent flexoelectric response is rationalized in terms of curvature-modulated BLM photo-potential. Possible applications of these new effects in membrane sensors (for sound, light, chemical species), in membrane actuators and their biological relevance are discussed.