Classical approaches for one-class problems such as one-class SVM and isolation forest require careful feature engineering when applied to structured domains like images. State-of-the-art methods aim to leverage deep learning to learn appropriate features via two main approaches. The first approach based on predicting transformations (Golan & El-Yaniv, 2018; Hendrycks et al., 2019a) while successful in some domains, crucially depends on an appropriate domain-specific set of transformations that are hard to obtain in general. The second approach of minimizing a classical one-class loss on the learned final layer representations, e.g., DeepSVDD (Ruff et al., 2018) suffers from the fundamental drawback of representation collapse. In this work, we propose Deep Robust One Class Classification (DROCC) that is both applicable to most standard domains without requiring any side-information and robust to representation collapse. DROCC is based on the assumption that the points from the class of interest lie on a well-sampled, locally linear low dimensional manifold. Empirical evaluation demonstrates that DROCC is highly effective in two different one-class problem settings and on a range of real-world datasets across different domains: tabular data, images (CIFAR and ImageNet), audio, and time-series, offering up to 20% increase in accuracy over the state-of-the-art in anomaly detection.