The article by W. Helfrich discusses the elastic properties of lipid bilayers, focusing on the three types of strain: stretching, tilt, and curvature. The author argues that curvature elasticity is the primary factor controlling the shape of vesicles (closed bilayer films) that are not spherical. Euler-Lagrange equations are derived to describe the shape changes under magnetic fields and excess external pressure. Magnetic fields can deform spherical vesicles into ellipsoids of revolution, and excess external pressure can make the spherical shape unstable at a certain threshold pressure. The spontaneous curvature of the bilayer can influence these effects. The article also discusses possible experiments to determine the elastic properties, including measuring the curvature-elastic modulus and spontaneous curvature. The strength of thermal fluctuations and their impact on vesicle shape are highlighted as important open questions.The article by W. Helfrich discusses the elastic properties of lipid bilayers, focusing on the three types of strain: stretching, tilt, and curvature. The author argues that curvature elasticity is the primary factor controlling the shape of vesicles (closed bilayer films) that are not spherical. Euler-Lagrange equations are derived to describe the shape changes under magnetic fields and excess external pressure. Magnetic fields can deform spherical vesicles into ellipsoids of revolution, and excess external pressure can make the spherical shape unstable at a certain threshold pressure. The spontaneous curvature of the bilayer can influence these effects. The article also discusses possible experiments to determine the elastic properties, including measuring the curvature-elastic modulus and spontaneous curvature. The strength of thermal fluctuations and their impact on vesicle shape are highlighted as important open questions.