Interpreting the inner workings of deep learning models is crucial for establishing trust and ensuring model safety. Concept-based explanations have emerged as a superior approach that is more interpretable than feature attribution estimates such as pixel saliency. However, defining the concepts for the interpretability analysis biases the explanations by the user's expectations on the concepts. To address this, we propose a novel post-hoc unsupervised method that automatically uncovers the concepts learned by deep models during training. By decomposing the latent space of a layer in singular vectors and refining them by unsupervised clustering, we uncover concept vectors aligned with directions of high variance that are relevant to the model prediction, and that point to semantically distinct concepts. Our extensive experiments reveal that the majority of our concepts are readily understandable to humans, exhibit coherency, and bear relevance to the task at hand. Moreover, we showcase the practical utility of our method in dataset exploration, where our concept vectors successfully identify outlier training samples affected by various confounding factors. This novel exploration technique has remarkable versatility to data types and model architectures and it will facilitate the identification of biases and the discovery of sources of error within training data.