Membrane structures have been used since the earliest of times. Until recently, their analysis has relied chiefly on trial and error; however, modern methods of analysis are evolving. The deformations are nearly always of the large rotation and/or strain type and are thus inherently nonlinear. Static analysis can be considered as a special case of the dynamic analysis. This paper is concerned then with reviewing methods of nonlinear dynamic analysis of membrane structures. Two problems of analysis are associated with membrane structures: (i) shape (or form) finding; (ii) response (deformation and/or stress) analysis. Shape finding (ie, determination of the surface geometry given an initial prestress, generation of cutting patterns, etc) is nontrivial but well documented in the literature and is not considered in this paper. In this review attention is instead focused on formulation of field equations, wrinkling analysis, fluid/structure interactions, material nonlinearities, and computational methods.