Domain adaptation in person re-identification (re-ID) has always been a challenging task. In this work, we explore how to harness the similar natural characteristics existing in the samples from the target domain for learning to conduct person re-ID in an unsupervised manner. Concretely, we propose a Self-similarity Grouping (SSG) approach, which exploits the potential similarity (from the global body to local parts) of unlabeled samples to build multiple clusters from different views automatically. These independent clusters are then assigned with labels, which serve as the pseudo identities to supervise the training process. We repeatedly and alternatively conduct such a grouping and training process until the model is stable. Despite the apparent simplify, our SSG outperforms the state-of-the-arts by more than 4.6% (DukeMTMC→Market1501) and 4.4% (Market1501→DukeMTMC) in mAP, respectively. Upon our SSG, we further introduce a clustering-guided semisupervised approach named SSG ++ to conduct the one-shot domain adaption in an open set setting (i.e. the number of independent identities from the target domain is unknown). Without spending much effort on labeling, our SSG ++ can further promote the mAP upon SSG by 10.7% and 6.9%, respectively. Our Code is available at: Https://github.com/OasisYang/SSG.