Abstract: We consider the discrete membrane model on the integer lattice. Analogously to the more famous discrete Gaussian free field, this random surface can be viewed as a multivariate Gaussian variable whose covariance matrix is the discrete bilaplacian Green's function. In dimension one, it was shown by Caravenna and Deuschel that this object converges to an integrated Brownian bridge. In higher dimensions we prove that, under appropriate rescaling, the model converges to the continuum membrane model. More precisely, we will show that the scaling limit in d=2, 3 is a Hölder continuous random field with covariance given by the biharmonic Green's function. On the other hand in dimensions larger than 4 the membrane model converges to a random distribution, also related to the biharmonic operator. Joint work with Biltu Dan and Rajat Subhra Hazra (ISI Kolkata).