Recently proposed consistency-based Semi-Supervised Learning (SSL) methods such as the Pi-model, temporal ensembling, the mean teacher, or the virtual adversarial training, achieve the state of the art results in several SSL tasks. These methods can typically reach performances that are comparable to their fully supervised counterparts while using only a fraction of labelled examples. Despite these methodological advances, the understanding of these methods is still relatively limited. To make progress, we analyse (variations of) the Pi-model in settings where analytically tractable results can be obtained. We establish links with Manifold Tangent Classifiers and demonstrate that the quality of the perturbations is key to obtaining reasonable SSL performances. Furthermore, we propose a simple extension of the Hidden Manifold Model that naturally incorporates data-augmentation schemes and offers a tractable framework for understanding SSL methods.