We present THUNDR, a transformer-based deep neural network methodology to reconstruct the 3d pose and shape of people, given monocular RGB images. Key to our methodology is an intermediate 3d marker representation, where we aim to combine the predictive power of model-free-output architectures and the regularizing, anthropometrically-preserving properties of a statistical human surface model like GHUM -- a recently introduced, expressive full body statistical 3d human model, trained end-to-end. Our novel transformer-based prediction pipeline can focus on image regions relevant to the task, supports self-supervised regimes, and ensures that solutions are consistent with human anthropometry. We show state-of-the-art results on Human3.6M and 3DPW, for both the fully-supervised and the self-supervised models, for the task of inferring 3d human shape, joint positions, and global translation. Moreover, we observe very solid 3d reconstruction performance for difficult human poses collected in the wild.