Recent advances in learning Deep Neural Network (DNN) architectures have received a great deal of attention due to their ability to outperform state-of-the-art classifiers across a wide range of applications, with little or no feature engineering. In this paper, we broadly study the applicability of deep learning to website fingerprinting. We show that unsupervised DNNs can be used to extract low-dimensional feature vectors that improve the performance of state-of-the-art website fingerprinting attacks. When used as classifiers, we show that they can match or exceed performance of existing attacks across a range of application scenarios, including fingerprinting Tor website traces, fingerprinting search engine queries over Tor, defeating fingerprinting defenses, and fingerprinting TLS-encrypted websites. Finally, we show that DNNs can be used to predict the fingerprintability of a website based on its contents, achieving 99% accuracy on a data set of 4500 website downloads.