Tension field theory has been used to study membrane wrinkle for a long time. This theory ignores membrane's bending rigidity, and assumes that wrinkling region is in an uniaxial stress condition. Wrinkles are oriented in the direction of the local major principal stress, and the minor principal stress, in the direction perpendicular to the wrinkle direction, is zero. Many wrinkle models are based on this method. They modify the constitutive relation or deformation gradient, then through numerical method, obtain the stress distribution and the direction of wrinkle. The main disadvantage is that it can not obtain some information of wrinkles such as wavelength, amplitude and number. Wrinkle analysis based on energy method first assumes the deforming pattern, and then obtain the expression of wrinkle's amplitude and wavelength through energy relations. This paper compares different models of membrane wrinkle, and discusses development trends of membrane wrinkle research.