This paper presents two new document ranking models for Web search based upon the methods of semantic representation and the statistical translation-based approach to information retrieval (IR). Assuming that a query is parallel to the titles of the documents clicked on for that query, large amounts of query-title pairs are constructed from clickthrough data; two latent semantic models are learned from this data. One is a bilingual topic model within the language modeling framework. It ranks documents for a query by the likelihood of the query being a semantics-based translation of the documents. The semantic representation is language independent and learned from query-title pairs, with the assumption that a query and its paired titles share the same distribution over semantic topics. The other is a discriminative projection model within the vector space modeling framework. Unlike Latent Semantic Analysis and its variants, the projection matrix in our model, which is used to map from term vectors into sematic space, is learned discriminatively such that the distance between a query and its paired title, both represented as vectors in the projected semantic space, is smaller than that between the query and the titles of other documents which have no clicks for that query. These models are evaluated on the Web search task using a real world data set. Results show that they significantly outperform their corresponding baseline models, which are state-of-the-art.