Modeling of thin elastic structures subject to large bending deformations, without much streaching and shearing, leads to (geometrically nonlinear) Kirchhoff plate theories with pointwise isometry constraint. We discuss reduced models for both single and bilayer plates, which give rise to minimization problems for the Hessian of the deformation with or without a spontaneous curvature tensor. We present a novel DG approach based on continuous piecewise polynomial elements of degree bigger than one for the ensuing fourth order problem. We prove its Gamma-convergence, and propose an iterative method that decreases the energy and yields stationary configurations. This work is joint with A. Bonito and D. Ntogkas.