This paper presents a deep semantic similarity model (DSSM) for recommending target documents to be of interest to a user based on a source document she is reading. We observe, identify, and detect naturally occurring signals of interestingness in click transitions on the Web between source and target documents, which we collect from commercial Web browser logs. The DSSM is trained on millions of Web transitions, and maps source-target document pairs to feature vectors in a latent space in such a way that the distance between source documents and their corresponding interesting targets in that space is minimized. The effectiveness of the DSSM is demonstrated using two interestingness tasks: automatic highlighting and contextual entity search. The results on large-scale, real-world datasets show that the semantics of documents are important for modeling interestingness and that the DSSM leads to significant quality improvement on both tasks, outperforming not only the classic document models that do not use semantics but also state-of-the-art topic models.