We ask the following question: what training information is required to design an effective outlier / out-of-distribution (OOD) detector, i.e, detecting samples that lie far away from training distribution? Since unlabeled data is easily accessible for many applications, the most compelling approach is to develop detectors based on only unlabeled in-distribution data. However, we observe that existing detectors based on unlabeled data perform poorly, often equivalent to a random prediction. In contrast, existing state-of-the-art OOD detectors achieve impressive performance but require access to fine-grained data labels for supervised training. We propose SSD, an outlier detector based on only unlabeled training data. We use self-supervised representation learning followed by a Mahalanobis distance based detection in the feature space. We demonstrate that SSD outperforms existing detectors based on unlabeled data by a large margin. Additionally, SSD achieves performance on par, and sometimes even better, with supervised training based detectors. Finally, we expand our detection framework with two key extensions. First, we formulate few-shot OOD detection, in which the detector has access to only one to five samples from the targeted OOD dataset. Second, we extend our framework to incorporate training data labels, if available. We find that our novel detection framework based on SSD displays enhanced performance with these extensions, and achieves state-of-the-art performance.