This paper reviews liposomes with crystalline phase and polymersomes exhibiting crystalline and thermotropic liquid crystalline phases in the membrane. Intriguing morphologies of vesicles are described, including spherical, ellipsoidal and faceted vesicles, produced by a large variety of amphiphilic molecules and polymers with nematic phase, smectic phase or crystalline phase. It is highlighted how the phase transitions and the phase grain boundaries could be used ingeniously to destabilize the vesicular structure and to achieve cargo-release under the action of external stimulation. These liposomes and polymersomes are responsive to physical stimuli, such as temperature variation, shear stress, light illumination, and magnetic and electric fields. These stimuli-responsive properties make them promising candidates as new smart drug delivery systems.