The convergence of Vision Transformers (ViTs) and self-supervised learning (SSL) has catalyzed a new paradigm in computer vision. While supervised ViTs often require massive, hand-labeled datasets, their self-supervised counterparts, particularly models trained with methods like DINO or MAE, have demonstrated an uncanny ability to learn rich, semantically meaningful representations from unlabeled images. This article surveys the remarkable "emerging properties" of these models, which go beyond simple image classification accuracy. We delve into phenomena such as the emergence of explicit scene segmentation within attention maps, the discovery of object boundaries, and the creation of highly transferable, linear-separable feature spaces. We analyze the mechanisms that give rise to these properties, including self-distillation and contrastive learning, and discuss their profound implications for both research and application in machine learning, particularly in data-scarce domains.